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 this fanfic, Naruto could potentially be the son of Tsunade. Tsunade had a soft spot for Naruto and they had a bond. It's possible that there was a hidden backstory where she was his mother. She was powerful enough to keep it a secret and Naruto's growth under her as a mother figure could be an interesting twist in the fanfic.
Maybe Naruto is the son of Orochimaru. I know it's a wild idea, but in a fanfic where the normal family ties are broken, Orochimaru could have used some kind of jutsu to create Naruto. He was always interested in experimenting and Naruto could be one of his strange creations. But this is just speculation in the context of this non - canon fanfic idea.
He could be the son of a rogue ninja who abandoned him in Konoha for some unknown reason. This would add an element of mystery to his past.
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, 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.
The story would change a great deal. For one, Naruto wouldn't have the same connection to the Nine - Tails as he does in the original. Minato sealed the Nine - Tails into Naruto, so without that relation, the whole dynamic of the Nine - Tails within Naruto would be different. He might not have the same power - up moments related to the Nine - Tails.
His father could be Ash from Pokemon. Ash has had so many adventures and it would be interesting if he somehow ended up in the Naruto world and had a child with a Naruto - world character. His mother could be a random ninja who had a connection with Ash.
One possible plot could be that with Minato and Kushina alive, Naruto grows up in a complete family. They could train Naruto together, passing on their unique jutsu. Maybe Minato could finally fulfill his dream of bringing long - lasting peace to the Hidden Leaf with his family by his side. And Naruto would have a different kind of confidence and growth, not having to face the loneliness he did in the original story.
If Minato and Kushina abandon Naruto in a fanfic, it could lead to a much darker Naruto. He might grow up more jaded and bitter. Without their love and support, he could be more easily influenced by negative forces. Maybe he'd have a harder time believing in friendship and loyalty, which are such important themes in the original story.
It might be due to jealousy. If Minato was getting more attention or praise in the village for his achievements while Kushina felt overlooked, that could create resentment. Say, Minato was constantly being hailed as a hero for his speed and battle tactics, and Kushina, who also had great power, felt like she was in his shadow.
It could show them feeling proud of Naruto's achievements. For example, when Naruto becomes Hokage, they might be seen with tears of joy in the fanfic.
One great fanfic is 'The Early Days of Naruto' which beautifully depicts Minato and Kushina's relationship with baby Naruto. It shows their tender moments together and how they start to teach Naruto about the ninja world from a very young age. Another good one is 'Naruto's Family Beginnings' where the focus is more on the family dynamic. You can really feel the love Minato and Kushina have for their baby. And then there's 'Baby Naruto's World' which goes into detail about how Naruto's presence affects the village even as a baby, and how Minato and Kushina are at the center of protecting and nurturing him.