Well, there's a fanfic called 'Bucky's Adoption Adventure'. In this, Bucky discovers a child in need and decides to adopt. It delves deep into his character, showing his protective and nurturing side. There are also some really good ones on platforms like Archive of Our Own. You can search using the tag 'Bucky Barnes adopts' and explore various fics that might interest you.
There is this great fanfic that I read. It's about Bucky Barnes adopting a teenager who has special powers. The story is really interesting as it shows how Bucky helps the teenager to control their powers while also dealing with his own past traumas. The relationship between them develops gradually and realistically. It also has some great action scenes along with the emotional moments that make it a really engaging 'Bucky Barnes adopts' fanfic.