I Don't Run An Orphanage!

Izuku Midoriya, couldn't be a hero. But despite this, he soon finds he's a magnet for trouble, particularly trouble involving children. There a lot's of children in the city with quirks that cause issues for them and the people around them. And if their parents won't care for them then he will! It may not have been the type of hero he wanted to be. But he's a hero none the less!
Author:Kyodon
You can also find this fiction in
https://m.fanfiction.net/s/13626213/63/
and at
https://archiveofourown.org/works/27421528/chapters/67028365