One possibility could be that Minato was under some kind of mind - control spell. Maybe an enemy of Konoha managed to manipulate him into thinking that Naruto was in danger by being in the village. So, Minato kidnaps Naruto to take him to what he believes is a safer place. But as the story unfolds, Naruto tries to figure out what's wrong with his father and tries to break the spell on him.
Perhaps in the fanfiction, Minato kidnaps Naruto because he discovers a prophecy that Naruto's presence in Konoha will lead to its destruction in the future. Minato, believing he can change Naruto's fate away from the village, takes him. However, Naruto resists, not wanting to leave his friends and the place he calls home. They then have a series of emotional exchanges as they struggle with their different beliefs.
In this fanfiction, it could be that Minato is from an alternate timeline where something went horribly wrong with Naruto's upbringing. He travels to the current timeline and kidnaps Naruto to raise him in a different way. He thinks that the way Naruto is being raised in this timeline will lead to his downfall. Naruto is initially confused but then decides to go along with Minato for a while to understand his motives better.
One possible plot could be that Tsunade kidnaps Naruto because she believes an enemy is after him and she wants to keep him safe in a secret location. She might think that by taking him away from the village, she can train him without any distractions or threats.
Well, it could be that Anko has some secret motive. Maybe she's being controlled by an enemy force who wants to use Naruto for some dark purpose. So she kidnaps Naruto to deliver him to this force.
Perhaps Naruto is trying to protect Ino in a really extreme way. He could think that there are threats to her life that no one else is aware of. So, instead of talking to her or her friends about it, he decides to take matters into his own hands and kidnaps her to keep her safe in a secret location. But this would obviously cause a lot of chaos among the other characters in the Naruto universe.
Maybe in the fanfiction, Kushina kidnaps Naruto because she believes she can protect him better away from the Hidden Leaf Village. She thinks the village has become too dangerous for him. However, Naruto doesn't understand her intentions at first and struggles against her. As the story progresses, he realizes her love and the real reason behind her actions.
Well, one possibility is that Minato arrives just in time to save Naruto from a powerful enemy like Orochimaru. He could use his Flying Raijin to quickly reach Naruto and then use his other jutsu to fend off the attacker.
One possible plot could be Naruto learning unique jutsu from Minato right from the start. Minato could teach Naruto how to use the Flying Thunder God Technique at an early age. This would change Naruto's battles significantly, as he could quickly move around the battlefield and surprise his enemies. He might also learn about Minato's leadership skills and how to handle difficult situations within the village, making him more respected among the villagers much earlier in the story.
Well, it could start with Naruto being in a situation where he feels lost about his own path. Then, he starts researching about Minato more deeply. He finds out about Minato's early struggles, how he overcame them, and his great contributions to Konoha. As Naruto delves into Minato's story, he realizes that Minato was a true hero in every sense. This realization makes Naruto look up to Minato, and he decides to incorporate Minato's values into his own ninja way.
Maybe there's some sort of misunderstanding or a powerful enemy who has framed Naruto. Minato, following the rules of the village, arrests Naruto. As Naruto is in prison, his friends try to find evidence to prove his innocence, and Minato gradually realizes he's made a mistake and starts to help them from the inside.
A 'Naruto Minato Revived' fanfiction could have a plot where Minato is revived in a time of relative peace. He has to adjust to the new world where his son is a hero. He could start mentoring the younger generation of ninjas in the Leaf Village, sharing his knowledge about sealing techniques and combat strategies. He might also be involved in some political intrigue within the village as some might fear his power or see him as a threat to the new order.
Another idea is that Naruto's strong will and determination somehow reach Minato in the past. Minato, inspired by this unseen force which is actually Naruto from the future, finds the strength within himself to overcome a seemingly impossible situation. This could be during the Nine - Tails attack on Konoha, where Naruto's spirit gives Minato the idea to seal the Nine - Tails in a different way that doesn't cost him his life.