For every life you save.. // Vigilante Deku AU

Deku is a short, scrawny and quirkless kid, everything the world defines as 'unnatural'.
He knows he can't get into UA, and even if he did he feared for the bullying. So, instead of fulfilling his wishes and getting into his dream school, he saves people in the dark of nights, killing villains who dare hurt innocent civilains.
When he tricks Overhaul into thinking he joined his group, and runs away with Eri, how long will he last before being murdered by the villain?
When he comes into contact with the League, will he finally meet who his father secretly was?
When he is taken into rehab by UA, will he find some sort of connection with the heroes, even though they treat him like a villain?

FT: DadForOne, Dadmight, Dadzawa, Adoptive brother Shigaraki and Toga x Deku.