Black Sheep is an oddball, which is fitting, given the theme of the trope itself. The description is broad, talking about all the ways in which a character can be an outcast among their family, even to the point of letting the kid be the one to outcast their family while the family still embraces the kid. However, the real life definition is much narrower and specifies they're the one of the family who gets targeted and singled out, usually unfairly, and often as part of a broader family dynamic. I should also note here that White Sheep, the supposed "counterpart", has no idea what Black Sheep means and thinks it's about an evil kid in a good family... and unless there was a weird description overhaul at some point, I have no idea why.

The wick check doesn't fully prove what I went in assuming: That most examples were going to follow the real-life definition. Instead, it's more or less used as "group oddball", but at least the real-life definition was more common than "evil kid" and "kid rejects family". Here's the run down, with the actual wick check in the sandbox linked:

• RL Definition: 5/50, or 10%
• Rejects Their Family: 2/50, or 4%
• Evil Kid, Good Family: 1/50, or 2%
• Group Oddball: 10/50, or 20%
• General Misuse: 6/50, or 12%
• ZCE: 23/50, or 46%
• Multiple Categories: 3/50, or 6%

It would be easy to just say "oh, change it to more properly fit the real-world term", but my first assumption is we can't really conform to a usage that isn't super popular. However, making it conform to the "group oddball" meaning would also be a bad idea because of the real-life term. What do?

Well, I propose we split off the "group oddball" trope if one doesn't already exist so that the misuse has somewhere to go, and then restrict Black Sheep to focus on the real-world definition. As for White Sheep... we'll have to tackle that another time once a wick check for it is produced.

1. Characters.Chrestomanci: In disgrace from his family. Low-context, but eh.
2. Characters.Titania Falls: While he isn't a complete outcast, he is easily the most disliked member of the Pines family and for a while has strained relationships with all of them sans Mabel (being Mabel) and Ford (since they don't know each other all that well).
3. Film.Incendies: Nawal. When Jeanne reveals that she's the daughter of Nawal, her distant family members say that Nawal brought shame to their family and kick Jeanne out of their house.
4. Series.Dopesick: One of Richard Sackler's possible motivations is that he's disliked and not taken seriously by the rest of the family, and creating a bestselling drug is his attempt to gain their respect. He manages to sway Kathe Sackler into siding with him by pointing out that, as a lesbian in a rich, conservative family, she's a bit of a black sheep, too, and that he respects her for being who she is.
5. VisualNovel.Nekopara: Maple and Cinnamon: Cinnamon is a Lovable Sex Maniac who turns a lot of things into sexual innuendos and gets lost in her fantasies. Maple is a no-nonsense catgirl with a calm head. They even happen to be breeds of cat whose ears curl in opposite directions. At one point, Maple is called the pride of the family while Cinnamon is called a disgrace to the family.

1. Literature.A Place Called Here: Sandy has been feeling like a fish out of water in her family since her childhood, because they don't understand her fascination/obsession with finding lost things. This made her leave her parents and birth town at 18, and as an adult she has a civil, though not really warm relationship with her parents.
2. WebVideo.An Ordeal In Onsondu: As of episode 33, she is also a foil to Aren. Both left their aristocratic elven families, becoming the Black Sheep of their clan in the process. However, Ife's reasons for leaving were rooted in moral objections, as her family is genuinely awful. In comparison, Aren's family is pleasant and warm, and Aren's departure was more related to shame about his identity and powers.

1. Film.Red Notice: Booth had issues with his policeman father, so he became a criminal. Hartley had issues with his criminal father, so he became a cop. Until The Reveal that he actually decided to become a better criminal. Tropeslashed with White Sheep; the Black Sheep part seems to be the "turned criminal" thing.

1. Characters.Fight For The Lost: Baz is an oddity among krogan. He's restrained, honourable and sincerely believes in fair play, even in combat. Currently a bodyguard for human gun shop owner. Ex Blood Pack.
2. Characters.Katmandu Other Tribes: According with the description given by Chief Pownetkee to Liska about Rakon's identity, the Red Canyon people are normally considered peaceful people, but Rakon is the exception on that rule. This is subverted like hell in the worst way possible, as they are also as bad as him, especially when they attacked the Highland tribe when their warriors were out to hunt.
3. Characters.Robin Tim Drake: Didn't feature much in Batfamily stories during the New 52 era, being more closely tied to the Teen Titans. The one character he was closest to was Jason, whose series Red Hood and the Outlaws was written by the same writer.
4. Characters.The Smeet Series: Unlike the rest of her race, Ilk doesn't discriminate because of one's height, she's pretty open-minded and overall she lacks the drive that leads the Irken race to subjugate 'inferior' species.
5. DarthWiki.Speed Sounds: The only good guy who descends from the City's Founding Father.
6. Film.Anvil The Story Of Anvil: When Lips' siblings are being interviewed, on-screen text shows they are all well-educated professionals. They note that Lips was never interested in following the conventional path and would have always pursued the arts, no matter what.
7. Manga.Delicious In Dungeon: Klingon Scientists Get No Respect: Dwarves value blacksmithing and mining above all other professions; Senshi's seen as an oddball at best for eschewing those in favor of hunting, cooking and farming.
8. Recap.Skins S 1 E 3 Jal: Jal, a female classical music player in a family full of male grime musicians.
9. Series.For The People: Allison is the only lawyer in a family of scientists and mathematicians.
10. TabletopGame.Invisible Sun: Apostates are vislae who refuse to align themselves with one of the four Orders of the Invisible Church; they can wield magic of any type and make their own discoveries, but lack the refinement or benefits that being a member of an organized Order grants. It can also make it hard for them to get along with dedicated members of an Order.

1. Aliens in Cardiff: What We Do in the Shadows follows the misadventures of a group of ancient, murderous vampires living as flatmates in Wellington, New Zealand. The spin-off TV show focuses on a different group who live on Staten Island, which, while technically part of New York City, is considered the Black Sheep of the Five Boroughs and often viewed as an extension of suburban New Jersey.
2. Anime.Pom Poko: Shoutout: To Ocean Waves of all things, especially considering its status as a Black Sheep in the Ghibli catalog: in a scene where the disguised Tanuki are doing a field test of their transformation, there's a poster for the film in the window of a convenience store, prominently displaying Rikako.
3. Film.Shin Kamen Rider Prologue: The Black Sheep of Kamen Rider? Or just covered in dried blood?
4. Manga.Kokkoku: Though the members of the Yukawa family are the main characters and normal people, it's later revealed Takafumi isn't entirely innocent. First, he summons Shouko's Herald family by testing how much bloodlust is needed for a Herald to show up (something which Sako calls him "sick" for). Then, he decides he wants to use the stone to cheat and steal so that his family can have a more prosperous life. ...I don't think this is the right trope.
5. Music.Deep Purple: Good luck finding a radio station that will play anything other than Machine Head, In Rock, and Burn.
6. Podcast.Four Player Podcast: Brad and Mike view this of Mass Effect 3. Nick might agree, but he's never voiced it.

1. Characters.Darksiders Horsemen: Is described as this in the novel.
2. Characters.Paragon 2016: Apparently, as her own uncle, Greystone, has imprisoned her multiple times. Isn't even confident.
3. Characters.SSX: According to him, he was.
4. Characters.Starjammers: His outlaw lifestyle downplays it, but he is loyal unto death to his sons, even Black Sheep Vulcan.
5. Characters.The Emiya Clan: Considers himself to be one to the rest of the Clan.
6. Characters.The Mindy Project: In his family, he's considered one. Though considering how awful his family is from his stories, it might be closer to a White Sheep.
7. Characters.Xiaolin Showdown One Episode Characters: Slightly implied since she did join a biker gang and why Clay nor their father mentioned her before.
8. ComicBook.Miracleman: Totally deconstructed. Like a real family, there is the Black Sheep and Dysfunction Junction, and plain weirdness.
9. DarthWiki.On The Edge: Ragtag Bunch of Misfits: The CSC, comprised of Kate, Mollie, Reilly, Delilah, Vera Jane, Lanie, Haley, Violet, Ai and Rachel. There's also the friends they make at Henie, Vanessa, Oz, and Jinx.
10. Film.Barefoot: Jay, compared to his more successful younger brother.
11. LightNovel.Inukami: Keita; it's implied his failure at attracting an Inukami and subsequent Black Sheep status broke him.
12. Literature.Children Of The Red King: Lyell Bone in the Yewbeam family; Bartholomew Bloor in the Bloor family.
13. Literature.Janie: Janie or Jennie when she rejoins the Spring family in Whatever Happened to Janie.
14. Literature.Varjack Paw: Varjak. Outside of Elder Paw, the rest of his family are either vain bullies or dismissive jerks that are obsessed with perfection. Partial context; doesn't tell us about if he's rejected them or got rejected or is just a good apple in a bad bunch.
15. Literature.Weetzie Bat: Witch Baby, lampshaded by Weetzie.
16. Monster.Sherlock Holmes: Jack Stapleton, real name Rodger Baskerville, wins the trust of the Baskervilles family while using an abused, trained hound to simulate the dark legend of the Hound of the Baskervilles.
17. Music.Sonata Arctica: Not in the straight sense of the trope, just that they got a song called "Black Sheep". Though the point of the song is this trope, kind of.
18. Recap.Lady Jane: Frederica breaks crucial rules of etiquette (particularly regarding interaction between men and women) like Marianne Dashwood, dares to show attraction to a man before he shows attraction to her like Catherine Moreland, is persecuted by a Wicked Stepmother-esque guardian like Fanny Price, is the Black Sheep of her family and criticized for her quietness and self-control like Elinor Dashwood and Anne Elliot, and is no dashing beauty (like her mother) who effortlessly charms men at first sight but is misjudged and dismissed as insignificant and undesirable in every way by her future husband until he learns the error of his first impressions like Elizabeth Bennet was, and most importantly, is determined to Marry for Love like any Jane Austen heroine. It only mentions the Black Sheep thing once and doesn't go into much detail beyond that she's criticized.
19. Roleplay.The Gamers Alliance: Jeremiah and Omaroch had to suffer a lot in their respective families.
20. Theatre.Icebound: Ben is described as this. He's been a drunkard and a hellraiser, and he's on the lam after getting drunk, getting in a fight, and torching the barn of the men he fought with.
21. Webcomic.Xenospora: Strike is this in the eyes of her mother.
22. YMMV.The Blue Bird: In The Betrothal, it's never specified why the Sick Man is so wicked. Nothing is said about his life beyond the fact that he was very sick, and his one fault in the actual play is picking Aimette for Tyltyl's future bride while the noble ancestors don't agree with him. Unlike the Rich Man, the Sick Man doesn't push Tyltyl for a Gold Digger marriage, and unlike the Drunkard and the Murderer, he doesn't attempt to grope Aimette himself. Nevertheless, he is treated as though he is as despicable as the other three Black Sheep ancestors.
23. YMMV.The Troy Saga: Kassandra. Afflicted with her Cassandra Truth powers at the age of three that makes it so that not only is she aware of when she's going to die but also the rest of her family, friends, and entire kingdom. It's also implied her powers are gradually killing her. She's also very self-aware how her facilitating between ominous predictions, half-intelligible gibberish, and then seeming perfectly normal makes her considered a Creepy Child and a Black Sheep of her family. In what way?

1. Characters.Kaiserreich China: Ma Zhongying was originally from the Ma Clique, but was expelled because he had extreme ambitions that led him to raid other Ma clique members. In addition, while the Ma Clique is already one of the more brutal warlord cliques in China, Ma Zhongying is considered one of the worst among them. I... am torn on this one, but I'll put it here because it's too broad for the other categories.
2. Characters.Kill La Kill Elite Four: Was a disruptive delinquent from a well-to-do family. Eventually, his father got fed up with him, punched him out, and challenged him to do something with his life if he was so sick of being The Un Favourite. Thus, Sanageyama formed the Northern Kanto Bancho Alliance. Seems to be both about a bad kid in a good family, and rejection from both ends.
3. Literature.Hercule Poirots Christmas: Harry abandoned all contact with his family years earlier and is considered a failure by pretty much everyone. Both forms of rejection here.