All Might tell Midoriya he can't be a hero when he's quirkless. Does that stop the green bean? Nope. Finding an abandoned toddler in an alleyway wasn't on his to do list though. But no one cared enough to care if he adopted the kid or not. And if anyone thought something small like a villainous quirk was enough to put Midoriya off, then they were very, very wrong.

After the sludge incident, Izuku Midoriya's dream was officially crushed. However, a later experience takes the boy in a new direction. Izuku had never really contemplated being a detective, but his whole life he'd only ever wanted to help people with a smile on his face. Thanks to some luck and an entire police station, Izuku's dream is reborn.

After an unforeseen chain of events, Class 1-A now resides in the world unlike their own, where heroes are not a paying job. And the only heroes are the unforgettable soldiers of justice, Kamen Riders! Join the heroes in training and the veterans of the Heisei era, as they will learn what it takes to be a hero.

Of which Izuku is the twin sister of Todoroki Shouto and is adopted by Midoriya Inko at birth. Story adopted from user ICanRememberThis.