Great Ape's Hero Academia

Izuku was never a normal boy, in fact he was strange from birth. He was born with a tail.

In case no one can tell, this was a crossover idea with dragon ball.

Izuku's Quirk will be based off the Saiyan race and if One For All exists in this fanfic, one of the following things might happen....

Izuku gets One For All and it fuses to his quirk allowing the ability to go Super Saiyan or it would "vanish" giving his quirk an ever growing power base of its own.

One For All goes to mirio.

One For All Isn't a transferable Quirk.