Naruto could pass on his determination. He's always been someone who doesn't give up easily, and Minato might inherit that. Also, his loyalty. Naruto is extremely loyal to his friends and the village, and Minato could grow up with those values. Maybe even Naruto's love for ramen would be passed on in some comical way.
Naruto could inherit Minato's calm and intelligent nature. Minato was known for his quick thinking in battle. From Mei, he might get her boldness. Mei was never afraid to speak her mind and take risks. So Naruto could be a combination of being smart in combat situations like Minato and fearless like Mei.
Yes, there are likely some fanfictions out there with such a concept. You can try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own. Just type in 'Naruto Father of Minato' in the search bar and see what comes up.
One possible reason could be for Naruto's protection. Maybe Minato knew of some great danger that was coming for Naruto and he thought that banishing him would keep him out of harm's way. Another reason might be related to some prophecy or hidden power within Naruto that Minato feared could be misused if Naruto stayed in the village.
The story could also start with a strange genjutsu or curse that alters reality. Naruto wakes up one day and suddenly he's in a world where he's Minato's father. He has to navigate this new family dynamic while also dealing with the political and ninja - related issues in the village. Since Naruto has always desired a family, this new situation could bring out new sides of his character, both in terms of his paternal instincts and his leadership within the family and the village.
The relationship can be developed by having Minato appear in Naruto's memories more vividly. For example, Naruto could start having flashbacks of Minato's training sessions or family moments that he didn't know about before. This would make Naruto feel closer to his father.
Minato could also teach Naruto about leadership. As the Fourth Hokage, he led Konoha. He could share his experiences on how to make tough decisions for the good of the village and its people. He might tell Naruto stories of past battles and how he strategized to win, which would help Naruto in his future as a leader in Konoha.
Well, it could be quite complex. Firstly, the writer would have to re - imagine the entire Naruto lore to some extent. Since Naruto is known to be Minato's son in the original series, for Naruto to be the father, there would need to be a major shift in the story's dynamics. It could involve a lot of changes in the relationships between characters. For example, how would Kushina react to Naruto being Minato's father? And how would Naruto, who has his own set of values and experiences from his own time, raise Minato? There are so many possibilities to explore.
One possible reason could be fear. If Naruto was 'godlike' in this fanfiction, his power might be uncontrollable and Minato, as Hokage, might feel it's a threat to the village. He could think that Naruto's power could attract too many dangerous enemies or cause destruction accidentally.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.
Naruto might become more calm. Minato was a very composed person, and if Naruto becomes like him, he'll lose some of his impulsive nature. For example, instead of rushing into battle head - first all the time, he'll start to think more strategically like Minato did.