There's a fanfic called 'Minato's Return'. In this story, Minato somehow returns and gets to see Naruto's growth. It's really interesting to see how he interacts with Kushina, who is also there in the story, and how they both guide Naruto in new ways. The descriptions of their family bond are heartwarming.
Well, in such a fanfic, Naruto could be the son of someone like Jiraiya. Jiraiya was very close to Naruto and taught him a great deal. He might have had a secret relationship that led to Naruto's birth. Another possibility could be that Naruto is the son of an unknown shinobi from a far - off village who somehow ended up in Konoha.
In a fanfic, Kushina might be depicted as a source of great wisdom for Naruto. Since she was his mother, she could pass on some Uzumaki family secrets or just some motherly advice. Minato could be the guiding force in Naruto's development as a ninja. His skills and experiences could be something that Naruto looks up to. Naruto himself should be a complex character, with his own insecurities and doubts at times, but always pushing forward because of his parents' influence.
On a more personal level, they could face internal guilt. As Naruto grows up and achieves great things on his own despite their neglect, Minato and Kushina may realize what they've missed out on. This realization could cause them a great deal of internal turmoil and regret for not being there for their son when he needed them.
In many Naruto fanfictions where Naruto meets Kushina and Minato, it often creates a very emotional scenario. Naruto finally gets to meet his parents who he has only heard about. It could be a heart - warming reunion where they share stories, hugs, and Minato and Kushina get to see how far Naruto has come.
One possible way this fanfic could go is that Minato and Kushina's spirits could be in a state of limbo and they are forced to witness Naruto's abuse. This could lead to a series of events where they try to find a way to communicate with Naruto or influence the situation to stop the abuse. Maybe they reach out to other characters in Naruto's life to help protect him.
One consequence could be that Naruto becomes an outcast in a different way. In the original, he was an outcast because of the Nine - Tails, but here, it could be because of his abandonment. He might not have the same dreams of becoming Hokage. Instead, he could be more focused on survival.
Minato would probably be very proud. He might notice Naruto's use of his own jutsu and be impressed by how Naruto has developed his skills. Kushina would be more emotional, maybe crying at the sight of Naruto growing up so well.
At first, Naruto and Kushina might start to distance themselves from Minato. They could avoid him and not talk to him as much. As time goes on, the hatred might grow deeper. Naruto could start to oppose Minato in public or in important village matters. Kushina might also try to influence others in the village against Minato.
Well, the story could develop in many ways. Maybe Naruto could be an orphan found by someone else in the village, like an old ninja who decides to train him in secret. This would change Naruto's backstory completely. He might not have the same kind of pressure or expectations that come with being the son of a famous Hokage. His character could grow in a different direction, perhaps being more independent from the start as he has to create his own identity without the shadow of his 'father' Minato.