In such a fanfiction scenario, the village of Konoha would be affected too. Minato is a respected figure. His abandonment could cause a scandal. Naruto might not have the same level of protection from the village elders. This could lead to different power dynamics within the village. Maybe other ninja clans would try to take advantage of Naruto's situation. Also, Kushina's family might react in various ways, some might try to find Minato and some might focus on taking care of Kushina and Naruto.
It could be a matter of prophecy. Minato might have received some sort of prophecy that staying with Naruto and Kushina would lead to the destruction of the village. So, in a misguided attempt to save Konoha, he abandons them. Or, there could be a power struggle within the village that makes Minato believe that leaving Naruto and Kushina is the only way to keep the peace. However, these are all just speculations within the context of fanfiction.
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.
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.
One possible reason could be some sort of dark influence or curse that makes her lose her maternal instincts. Maybe a powerful enemy targets her and in order to protect Naruto from further danger related to her, she feels forced to abandon him. Another reason might be that she is made to believe false information about Naruto, such as that he will bring great disaster to the village in the future.
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.
In many Naruto fanfictions, Minato is often portrayed as an even more brilliant strategist and a loving husband. He might be shown using his Hiraishin no Jutsu in creative ways to protect Kushina. For example, in some stories, he uses it to surprise her with little gifts or to show up just in time when she's in danger.
A fanfiction could center around a family training session. Minato trains Naruto in advanced ninjutsu techniques while Kushina teaches him about the Uzumaki clan's secrets. This would not only strengthen their family bond but also make Naruto an even more powerful ninja.
Well, I really like 'The Uzumaki Trio'. In this fanfiction, it shows the strong family unit of Kushina, Minato, and Naruto. It has great character development and some really touching moments. 'Minato's Promise' is also good. It's about Minato making a promise to Kushina before his death and how Naruto discovers this later. And 'Kushina's Strength' is a fanfic that emphasizes Kushina's power and how she and Minato complement each other.
In a fanfiction, perhaps Minato and Kushina are resurrected during a powerful enemy attack on the village. Naruto is in the middle of the battle when he suddenly sees his parents. At first, he can't believe it. Kushina runs to hug him tightly, while Minato stands there with a proud look. They then join the fight together, using their combined skills to defeat the enemy and have a moment of family reunion.