There were a couple of things that Midoriya Izuku had been told about his father: 1) He lived and worked overseas. 2) His quirk is breathing fire. But one of those is a lie to protect him from the knowledge that young Izuku was actually the son of the Number One hero: All Might.
And Izuku's life suddenly gets turned upside down when All Might mysteriously ends his decade-long stay in America and returns to Japan for a reason that everyone can only guess at.
My Hero Is My Dad? is a My Hero Academia fanfic by LightSage89 where All Might is actually Izuku's father. Hisashi Midoriya does not exist in this AU, all that remains of him is his fire breathing quirk, which Inko tells Izuku's doctor that his father has, since she can't tell the doctor about All Might's quirk.
The fanfic is the first in a series followed by My Teacher Is My Dad?!?
This fanfic provides examples of:
- Amicable Exes: While Inko and Toshinori are neither dating or have any intentions of getting married, they are still on relatively good terms.
- Contrived Coincidence: The fact that Izuku became a super fan of All Might happens with the complete lack of knowledge that he is also his father.
- For Want of a Nail: Because he has known All Might for far longer, Izuku has had years to train to be able to use One-For-All, having been given personal access to All Might's professional gym. While in-canon Izuku received One-For-All the same day as the UA Entrance Exam, here he is given it ten months in advance, allowing him time to learn how to use it more properly and securing the No. 1 spot on the entrance exam scoreboard.
- Izuku is transferred to a higher quality middle school, meeting and befriending Tenya Iida and Momo Yaoyorozu much earlier than canon. This also means that Bakugo has a much smaller presence in his life, Izuku having much more confidence.
- Heroic Lineage: The fact that All Might's own son has the right moral character to also be the successor of his quirk speaks for itself.
- A Mistake Is Born: Izuku was unplanned, though that does not make him any less loved by either of his parents.
- Secret Keeper: Izuku's middle school caters to a lot of children with pro-hero parents, so the teachers are sworn to secrecy in the case of Izuku's lineage.
- Momo was able to correctly deduce that his father was All Might just by comparing pro-heros with Super Strength quirks powerful enough to take down the Zero-Pointer. She and Tenya agree to keep this a secret.
- Strong Family Resemblance: Izuku takes mostly after his mother, making it easier to hide his connection to All Might. This is addressed by Recovery Girl when she meets him.Recovery Girl: And this is the boy that I've heard so much about? Never would have guessed this was your son just from looking at him.
Izuku: I... take after my mom, mostly.