Jethro Pelsman's father in Lost Cause is a drunk who physically and mentally abuses his poor son, leading to Jethro's inability to socialize, connect with others and a fear of falling in love.
Oasis' (adoptive) father in Sluggy Freelance uses mind control technology to turn her into his slave and personal assassin, who he plans to use to fulfill various fantasies.
To a lesser extent, it's heavily implied that Riff's mom, Dr. Lorna, deeply screwed him up when he was a kid. If she treated him anything like how she treats every other human being on the planet, then it's amazing he's not an even madder scientist than he is now. One confirmed instance is, well... She has a tazer that she uses on people on those occasions when she actually loses an argument. Riff won an argument about him getting a pony back in kindergarten. His memory immediately after that is a haze.
Leeza's father, Admiral Blake, in Terinu is implied to have merely been an Absent Parent when she was growing up. Now that she's an adult he's rebounded into a Manipulative Bastard, getting her fired when she thwarted his plans for Teri, sticking her with the boy's guardianship so he could still keep an eye on them both, culminating in arresting her and sending her to prison when she threatened to go public with the news that humanity wiped out Terinu's race.
The Order of the Stick: The only way in which Roy's father seems to care at all for either of his children is the extent to which they follow in his footsteps as a wizard. He has nothing but scorn for his eldest son Roy, who elected to take up the family Ancestral Weapon as a Fighter, and favors his spoiled Libby of a daughter instead (and almost never uses the words "crushing disappointment" when talking about her). Oh, and his second son? The fact that he ignored Roy's pleading led to his death.
So much so that when Roy dies, he offers his father a bargain: Roy will only cooperate if his father agrees to go away and leave the entire family alone for eternity. For double points, Daddy jumps on the bargain and scoffs that Roy made his price so low.
Roy Greenhilt: I don't know what's more depressing: That you agreed to that so easily, or that I knew that you would when I proposed it.
Haley's father seems to have crippled her ability to interact with others honestly due to the paranoia that came as a result of living as a member of the Thieves' Guild. Ian meant well, but had different, rather family unfriendly values he tried to teach to his daughter. When he finally appears, it seems he still loves Haley very much (although the feeling isn't entirely mutual). To his credit, unlike the other examples here, he realizes he screwed up and makes amends with Haley, encouraging her to live her life how she chooses. The two part on good terms.
Elan's father General Tarquin is a double subversion. While he's very clearly evil, he also seems to care about his son to at least some genuine extent. Later played straight when we get to see why Nale turned out the way he did. Then Tarquin reveals he's such a control freak he's prepared to murder all of Elan's friends to force him into the protagonist seat. As Elan continues to defy him, he gets so pissed off that he attempts to murder Haley and chop off Elan's hand.
In Dreamkeepers, there's 2 variations going on: one is physically abusive (Grunn), the other shuts his daughter in and isolates her from the outside world (Viscount Calah).
What Birds Know: Dores' parents are both pretty bad, but her mother is an outright Jerkass who shows absolutely No Sympathy for her daughter. As far as she's concerned, Dores is an utterly worthless waste of space while Ian is her pride and joy. While the other parents are concerned by the girls' prolonged absence, Dores' mother just harps on about how she's going to punish her once she gets back and tries to shoot down everyone else's attempts to put together a search party.
In Kagerou, Kano's father was this. Though only a few details have been given, it's been revealed that Kano's father shoved him into a morgue box with a dead body in it, which is likely the cause for a large part of Kano's mental trauma.
In Voodoo Walrus, it's been suggested that Creep Knight's father has disowned him and refused to respect his choice to become a writer over being part of the Liechtensteiner royal family. Yet his father regularly sends mercenaries to test his son's mental and physical mettle and attempts to drag him back home.
Quain'tana does not have a good track record with children, let's just say. To list the ways she screwed up her kids:
Syphile: Physically beat her, verbally berated her and handed her over to Sil'lice for "tutoring".
Mel'arnach: Imprisoned her and had her beaten for disobeying, and it's also implied that she had her men rape her in an attempt to conceive an heir. She also took Mel's child, Ariel, to raise as her own daughter.
Ariel: Took her away from Mel, her mother and handed her over to Syphile to raise (unsurprisingly Syphile did a terrible job and gave Ariel much the same treatment she herself had received). Didn't even see her for 10 years, and rejected her as a suitable heir until she killed a boy who had tried to kill her in a Sadistic Choice between him and one of her few allies. That said, Ariel seems to have grown into a much more well-adjusted person than her sisters and has a rather obvious case of hero worship for her mother, although the fact that she didn't spend anywhere near as much time in her care as Mel or Syphile did likely didn't hurt.
Her other children seem to have fared pretty well, considering, likely due Laele having been essentially Quain writ small and Kiel'noz being an indispensable voice of reason in the clan—and even he admitted that Quain was a horrible mother.
Snadhya'rune impressively manages to top Quain'tana in this regard. She never saw her daughter Kalki as anything but a tool. When she decided Kalki had become a liability, she used a summon to tear Kalki to shreds without batting an eyelash.
Luna Travoria from Dominic Deegan was emotionally abused by her mother in hopes that she would commit suicide while a knight was visiting, ensuring a hefty payout from the government.
Mitch and Jonas from Long Exposure both struggle or have struggled with emotionally and physically abusive parents. Mitch had a physically abusive stepdad who he stabbed after seeing him punch his mother, which left him with a juvie sentence, PTSD, and rumors that turned him into The Bully. Meanwhile, Jonas has emotionally distant foster parents and one over controlling foster dad making him the meek, needy nerd he is today.
Androssi Zahard from Tower of God and her adopted sisters were forced to fight each other by their father on a daily basis to decide which one would become a Princess of Zahard.
This is a rather common occurrence in the 10 Great Families.
The children of Hendo Lok Bloodmadder must die early because that is the condition he must fulfill to be immortal.
Koon's mother drove him to excel and be as ruthless and manipulative as she was. Until he'd had enough and used everything he'd learned to run away from home and steal a lot of expensive items on his way out that is...
El Goonish Shive: Damien ended up making himself a sort of twisted father figure to Grace and her brothers, but there is nothing "fatherly" about him at all. He is an abuser pure and simple, able to control his "children" through fear and constantly hitting them whenever they displease him. And like any parent whose children are young enough, he's too powerful for them to do anything about it.
Also, he intended to use Grace for breeding so he would have been a sexual abuser as well.
Grey is...: Black got severely beaten by someone in his home right up until he graduated from high school and moved away with White. We are not told directly but it is implied that the one abusing him was his dad.
Homestuck has a few variations on this theme; the most extreme is probably Vriska Serket's guardian, which forces her to capture hundreds of other children to feed it, but others include Dave's Bro (regularly beats the crap out of him and fills the apartment with creepy puppet porn, though it's mostly played for laughs) and Gamzee's lusus (just never there). It's unclear whether Rose's mom is actually the master of Passive-Aggressive Kombat that Rose makes her out to be or if she's honestly trying to connect with her, but either way she's perpetually drunk and on the negligent side. The introduction of Roxy, a teenage version of Rose's mom, and the revelation that her interests are all genuine instead of her trying to mock Rose, seem to heavily indicate the latter.
Later, someone managed to beat Vriska's lusus to the "Worst Parent of the Year" award: Doc Scratch, in caring for Aradia's ancestor the Handmaid. He keeps her locked in a tiny room, and when she gets out of line, he teleports her to outer space.
Silver's adoptive father in Ball and Chain forced her to compete in to-the-death gladiator matches from a fairly young age.
In Last Res0rt: Jason's mother is revealed in this flashback as a rather vicious (and at least physically abusive) Djinn. The fact that Jason has held onto his Mother's jacket so tightly ever since indicates some serious Parental Issues...
Charlotte's mother is shown to beat her daughter when she does or seems to do things wrong, and it is very heavily implied that one of Charlotte's parents sexually abused her as a child too.
Helen's parents treat her as The Unfavorite in their household and give her a conditional love response when she is unable to complete an age-inappropriate task. No wonder she's turned into an Extreme Doormat.
Marshall's mother, Charisma, is usually just neglectful, but she has gone into emotional abuse too on occasion, telling her son to his face that he was put on earth to slow her down. When Aggie's father, Nick told her to look him in the eye and tell him that she wouldn't be happier if both their children didn't exist, she couldn't do it.
Jamie's mom in Khaos Komix, who belittles him constantly and on multiple occasions beats him or physically harms him in other ways. She is also so selfish that she values her own reputation over bringing the man who raped her son to justice. At one point someone threatened to call social services on her, though that never went anywhere.
Pv P gives us Jade's mother. Her first appearance has her cancelling Jade's wedding, being openly emotionally abusive, and generally insulting everyone. When Jade told her she was pregnant, she tried to force her to move back home.
Norbert Olsen in The Overture physically and verbally abuses his son, Richard. Later, Norbert abandons his son in the wilderness and threatens to kill him if he returns home.
In Modest Medusa, the titular character's mother turns out to have dozens of daughters. So she feels no remorse about eating them alive whenever she feels peckish.
Distortion Nuzlocke has Johnny's dad, who's imagined as Giovanni. He outright tries to kill him at one point.
Anthony Carver of Gunnerkrigg Court is of the emotionally abusive type. While it appears that he does care about his daughter Antimony in some way namely coming back to the Court in exchange for keeping her from getting expelled for cheating, it's only when he's drunk in front of his best friend that he admits the choices he made in abandoning her, nearly killing her in a misguided attempt to bring her mother back from the dead, and humiliating Annie in front of her class, were horrible choices. While he is a deeply flawed and neurotic man and regrets his choices, he also realizes he's a horrible parent and thinks that it's better to let everyone think the worst of him and keep his daughter at arm's length.
Mool Byhung from Welcome To Room 305 was beaten by his father and kicked out of his house after he came out as a trans man. As an adult he lives with his brother, who was also abused.
Schtein's mother from String Theory, both mentally and physically. She believed showing your children affection gave them unrealistic expectations of the adult world. Might not be so far from the truth considering what kind of world they live in.
Benni's father from Forest Hill was not only physically abusive and neglectful to Benni but as went so far as to force Benni to have sex with men for money on a regular basis, to the point that Benni believed that it was normal for children to have sex with adults for money.
Emily's mother leaves her alone for months at a time and has made her feel unwanted her whole life.
Rain's father is heavily implied to have been physically and emotionally abusive, and abandoned his 12 year old child one day without a word.
Maria and Rudy's parents are cold towards them in general for being gay, but their father officially crosses this line when he begins doing research on camps for "curing" homosexuality and trying to isolate them from their friends after Maria comes out and Rudy breaks up with Rain.
My Mama's a Weeaboo by Stefano Collavini has the titular character. The comic starts with her dressing her daughter in ridiculous outfits and ends with her having the doctors put her on so much medication that she's a doll. Just like Mama wanted. The comic subtly implies that Mama's abuse goes back for years to keep her daughter under her thumb.
Charby was a slave from infancy aboard Captain Robert Black's ship and was regularly beaten, tortured for entertainment and had to fight with dogs for scraps of food. The man thought teaching him to read was enough to constitute parenting.
There are also a surprising number of unsupervised children who make their way into the forest, which is known to contain things which eat and attack humans even if the general populace thinks those things are bears, wolves and snakes.
In Megan Kearney's Beauty and the Beast, we eventually learn that the Beast's mother abused him verbally, psychologically and sometimes physically throughout his human years. When he finally stood up to her as a young man, she attacked him with a dagger, driving him to the suicide attempt that caused his transformation.