It could strengthen their bond. By being interested in fanfiction about Naruto, Minato shows that he's deeply invested in Naruto's story, which Naruto might appreciate.
Minato's obsession with Naruto fanfiction can have a complex effect on their relationship. If Minato shares his thoughts and feelings about the fanfiction with Naruto, it can create a new level of intimacy. Naruto might be flattered that his father is so interested in stories related to him. However, if Minato becomes too consumed by the fanfiction and starts to expect Naruto to be like the versions in the stories, it could cause some strain. But if they approach it in a healthy way, for example, using the fanfiction as a starting point for discussions about Naruto's hopes and dreams, it can definitely strengthen their connection.
On one hand, it might bring them closer. Minato's interest in Naruto fanfiction could lead to interesting conversations between them. They could discuss different fan - created stories, and Naruto might feel more understood by his father. However, it could also be a bit strange for Naruto at first. He might feel a bit self - conscious about his father reading all these fictional stories about him. But overall, if they communicate well about it, it can enhance their relationship.