Midoriya Mermaid Quirk AU
For convenience, this is a female Midoriya AU. Midoriya developed her quirk at six years old. She was taking a shower when suddenly she was falling and had a tail instead of legs. Having thought she was quirkless, this obviously freaked her out. Her quirk has several parts to it: She is stronger than a normal person, especially her tail; she obviously has a tail, which is green with scarlet fins and is hard to injure because of the armor-like scales; she can breath under water; she has hydrokinesis, but there has to be water already there for her to control it, she doesn't generate it.
She didn't know how to turn back, and stayed in that form for seven years, which meant she basically lived in the bath tub. She and Bakugou became friends again, and he became her pseudo brother. Unfortunately, at thirteen, her apartment caught on fire. She tried to save her parents, and dragged herself out of the tub. A flaming beam fell on top of her parents and she lunged for them to try and move them out of the way. This is when she turned back, but turning back took a lot of energy. She didn't manage to save her parents, which absolutely crushed her. She became depressed and lost interest in becoming a hero. She did pick up an interest in inventing, and eventually became interested in becoming a hero again.
Also, she's Kouta's cousin. The water horse duo was her aunt and uncle, and Hisashi had a similar quirk to Kouta's, only he could shoot water out of his mouth.
She doesn't make it into the hero course right away, but she does get into the support course. She wins the sports festival because Todoroki's fire melted all of the ice, giving her water to control, so she fights Bakugou. She uses a bit of an underhanded trick. She starts crying during their match and he immediately stops what he's doing to comfort her because she's like his little sister, and she throws him out of the ring(?). Shinsou was in the hero course in her place. Winning the sports festival gets her into the hero course, but she has a different schedule than the other hero course kids so she can continue her support course classes.
Aizawa eventually adopts her. He's married to Yamada in this AU and they adopted Shinsou too. Eri gets adopted later. Kirishima gets One For All in this AU.