One possible plotline could be that Minato and Kushina focus on teaching Naruto advanced chakra control. Since Minato was known for his Flying Thunder God Technique which required precise chakra control, he could pass on those skills. Kushina, with her strong chakra, might teach Naruto how to better harness his own Uzumaki chakra reserves. For example, they could start with basic exercises like tree - walking and water - walking, but with a twist. Minato could show Naruto how to use his chakra in a more efficient and strategic way during these exercises, preparing him for more complex jutsu later.
One possible plotline could be that Minato and Kushina train Naruto to master his chakra control more effectively. They might use their own unique jutsu and skills to teach him. For example, Minato could teach Naruto advanced space - time ninjutsu techniques that he himself was famous for, like the Flying Thunder God Technique. Kushina, on the other hand, could focus on helping Naruto understand the power of the Nine - Tails better and how to use its chakra in a more harmonious way. This could involve special training sessions where Naruto has to learn to balance his own chakra with that of the Nine - Tails under their guidance.
There might be a very dark and twisted fanfiction like that. It could be that Naruto is tricked into believing that Minato and Kushina are some kind of threat to the village or to his friends. So in a moment of confusion and misinformation, he takes drastic action. But this goes completely against Naruto's character in the original series.
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.
One interesting plotline could be Minato and Kushina returning during the Fourth Great Ninja War. They could turn the tide of the battle with their powerful skills. Minato's Flying Raijin would be a great asset, and Kushina's chakra chains could help in restraining powerful enemies. Another plot could be their return and how they interact with Naruto, teaching him new jutsus and sharing their experiences.
A possible plotline is that Naruto gets adopted by a group outside the village. He grows up learning their ways and becomes a sort of outcast from Konoha. Then, he could return to the village with a different set of skills and a new perspective. Or, he might develop a vendetta against Konoha for allowing his abandonment and try to take revenge in some way.
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.
The family dynamic in fanfiction could be quite interesting. Minato could be a strict but fair father, pushing Naruto to be the best ninja he can be. Kushina would balance this with her motherly love, always there to comfort Naruto when he fails. They would celebrate Uzumaki traditions together, and Naruto would learn about his parents' pasts. He would look up to Minato as a great Hokage and to Kushina as a strong - willed Uzumaki. Their family would be a source of strength for Naruto as he grows up in the ninja world.
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.
One possibility is that Naruto has an out - of - body experience and is able to communicate with his parents in a spiritual realm. They could give him advice on how to deal with his enemies and his inner demons.
One possible reason could be a misunderstanding. Maybe Naruto gets involved in some dangerous situation and they disagree on how to handle it. For example, if Naruto wants to take on a powerful enemy alone but Minato and Kushina think it's too risky.