From what I can remember Bucky and Steve live together and Bucky is the first to meet the girl she skinny and reminds him of Steve. She in the same building and the first time they meet I think she was sitting on the stairs reading. She lives with her aunt who isn't really there and when she is she is sort of abusive. The girl spends a lot of time with Steve and Bucky and from the last thing that I remember reading it was sort of getting to the point that they might adopt her or take her in. Steve and Bucky were still part of the Avengers. I read the fic on AO3. If anyone recognizes the fic that would be great.
So I found the fic. It is I Found It All On My Own by Karou001