One possibility is that Minato takes Naruto away to a secret training ground. There, he could start to teach Naruto advanced jutsu that he never got to pass on before. This would be a way for Minato to make up for lost time and help Naruto become even stronger.
Well, one possibility could be that Kushina takes Naruto away to protect him from the dangerous world of shinobi. Maybe she wants to raise him in a peaceful place away from the constant threats and battles in the Hidden Leaf Village.
It might develop with Naruto being initially confused and a bit angry at being taken away. But as Minato starts to show him new techniques or tell him stories about his past, Naruto would gradually come to understand. For example, Minato could show Naruto how to better control his chakra, which would be a major development in the fanfiction. And as they spend more time together, their father - son relationship would strengthen, which would be a central part of the story's development.
One possible reason could be fear. Minato is a very powerful shinobi, and Naruto might be scared of him for some reason. Maybe he has heard stories about Minato that made him afraid.
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.
One possible consequence could be that Naruto grows up away from the influence of Konoha's shinobi culture. He might develop a different set of values and skills. For example, without the guidance of Iruka and Kakashi, his understanding of ninjutsu and teamwork could be very different. Also, his relationships with characters like Sasuke and Sakura would be greatly affected. Maybe he wouldn't have the same rivalry with Sasuke, and his bond with Sakura might not even form.
Well, it could be that Naruto, under Minato's training, quickly masters powerful jutsus. He might learn advanced space - time ninjutsu faster than in the original story. With Minato's guidance, Naruto could also develop unique combat strategies, making him seem godlike in battles against tough opponents like the Akatsuki members.
Perhaps in this fanfiction, Minato and Kushina leave Naruto because they are cursed. They fear that the curse will harm Naruto if they stay close. So, they go into exile. As Naruto grows up, he starts to discover clues about his parents' real reason for leaving and sets out on a quest to find them and break the curse. This could lead to many adventures and character - development moments for Naruto.
Well, one possible plot could be that since Naruto is Minato's brother, he is not ostracized by the village. Instead, he is seen as a potential heir to Minato's legacy. This would change his entire character arc. He might not have the same drive to prove himself, but rather focus on living up to Minato's name. There could also be a plot where they face a common enemy together, and Naruto's bond with Minato helps him unlock new powers or techniques. Another aspect could be the exploration of their family secrets and how it impacts the whole Hidden Leaf Village.