Perhaps in this fan - made story, the world has been altered in such a way that Naruto is born as a female and she discovers Minato as an orphan. She decides to adopt him out of a sense of duty or a connection she feels to her own past. She would then raise him with her own set of values and ninja skills, which would be really interesting as Minato would be influenced by Naruto's different perspective.
In this fanfiction scenario, it could be that female Naruto exists in an alternate dimension where the normal rules of time and family don't apply. She might come across a young Minato who is in need of a family. Since Naruto has always known the pain of growing up without parents, she takes him in. This could lead to a whole new set of adventures and relationships as they both navigate through the ninja world together, with Naruto being both a mother - like figure and a ninja mentor to Minato.