One possible plotline could be that Minato sees Sasuke as a threat to Naruto in some way, perhaps thinking Sasuke's pursuit of power might harm Naruto. So he constantly tries to keep them apart. But Naruto and Sasuke's bond is too strong and they resist Minato's overprotectiveness. Eventually, Minato realizes that their relationship is something that can't be broken and he should trust in Naruto's judgment.
One reason could be guilt. Since Minato wasn't there for Naruto when he was growing up in the original story, in the fanfiction, he might be overcompensating for that lost time. He feels like he has to make up for all those years he wasn't around to protect his son.
One possible plotline could be that Minato and Yukari go on an adventure together to discover a new Sekirei. They might face various challenges along the way, like other groups who are also after the new Sekirei. This could test their friendship and their skills as Sekirei handlers.
There might be a very dark and twisted fanfiction like that. It could be that Naruto is tricked into believing that Minato and Kushina are some kind of threat to the village or to his friends. So in a moment of confusion and misinformation, he takes drastic action. But this goes completely against Naruto's character in the original series.
Perhaps Naruto, after being abandoned by Minato, falls in with a group of outcasts. Together they form a sort of family of their own. Naruto's natural leadership and kind heart start to shine through as he tries to protect this new family. As he uncovers more about his past and Minato, he has to decide whether to forgive his father or hold on to his anger. This internal struggle could be a major part of the fanfiction.
One possible plotline could be them working together on a mission in the Naruto world. Maybe they have to rescue some hostages or retrieve an important item. Another could be a story about their friendship growing over time as they share their experiences and knowledge with each other.
Well, in the fanfiction world, Minato might be overprotective of fem Naruto because he lost her once. Maybe there was some kind of incident in the past where Naruto was in great danger or even 'died' briefly. This made Minato extremely paranoid about losing her again, so he goes overboard with the protection. He might also be influenced by the fact that as a female in their world, Naruto could face different and perhaps more complex challenges than if she were male, like discrimination or special treatment from certain groups.
One possible plotline could be that Fen Reader has some special ability or knowledge that Team Minato needs. Maybe Fen Reader can see the future and warns Team Minato about an upcoming danger. Another could be that Fen Reader is from another dimension and gets lost in the Naruto world where they encounter Team Minato and end up joining them on a mission.
One possible plotline could be that Naruto gets trapped in Minato's memories and has to find a way out. While inside, he relives important moments from Minato's life and gains new powers or knowledge.
A possible plotline is that Naruto gets adopted by a group outside the village. He grows up learning their ways and becomes a sort of outcast from Konoha. Then, he could return to the village with a different set of skills and a new perspective. Or, he might develop a vendetta against Konoha for allowing his abandonment and try to take revenge in some way.
Well, Minato might constantly be by Naruto's side in the fanfiction. He could prevent Naruto from taking on any dangerous missions, even if Naruto is capable. For example, he may interfere when Naruto tries to join a risky battle against a powerful enemy, saying it's too dangerous for him.