Perhaps it's because Naruto represents the future of the village in a more direct way. Minato sacrificed himself for the village, and Naruto is like the continuation of his legacy. Kushina, while important, may not be as central to Minato's view of the village's future as Naruto is. So in fanfics, this could be a reason for Minato to like Naruto more.
In fanfics, Minato may like Naruto more than Kushina because Naruto has faced so many challenges alone. Minato, having lost his life early, wasn't there to protect Naruto as he grew up. This might make Minato feel a sense of guilt and at the same time a great admiration for how Naruto has overcome all the difficulties. Kushina, on the other hand, didn't have the same kind of story in relation to Minato in the fanfic's narrative, which could lead to Minato having a stronger preference for Naruto.
Well, in some fanfics, Minato might see more of himself in Naruto. Naruto has his determination and the will to protect the village just like Minato did. Also, Naruto being his son, he could have a special connection that he doesn't have with Kushina in the same way. Maybe Naruto's journey to become a great ninja reminds Minato of his own past, so he has a stronger liking for Naruto.
In some fanfics, Naruto might be made to hate Minato and Kushina due to a sense of abandonment. If the story is written in a way that emphasizes how Naruto grew up alone and suffering, he could project his anger onto his parents for not being there for him. For example, he might think that if they were alive, he wouldn't have had to endure the taunts and loneliness in the village.
One possible reason could be a miscommunication in the fanfiction. Maybe some secrets were kept from Naruto about his parents that made him feel betrayed when he found out, thus leading to hatred.
Another popular fanfic is 'Minato and Kushina's Legacy in Naruto'. This one explores how Minato and Kushina's influence on Naruto is not just about power but also about values. It has a long - running plot that unfolds as Naruto grows, and it has a great following among Naruto fans.
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.
One possible reason could be a misunderstanding. Maybe Minato thought Kushina had done something to endanger Naruto when in fact she hadn't. In the heat of the moment, he lost his temper and slapped her.
The theme of legacy is also quite common. Since Minato is the Fourth Hokage, fanfics might explore how he wants Naruto to carry on his legacy. And Kushina's strong will also gets passed on to Naruto in these stories. They also often show the simple joys of family life, like spending time together at home, which is a contrast to the dangerous ninja world outside.
Often in fanfiction, the resemblance between Naruto and Minato can be for emotional impact. When other characters see Naruto looking like Minato, it can stir up memories and emotions related to Minato. This can create interesting character interactions, like when the older generation sees Naruto and is reminded of Minato. It also adds an extra layer to Naruto's character as he might start to understand more about his father through this physical resemblance, like how people might react to him differently because of it.
Another way is to join Naruto - related fan communities on social media platforms such as Reddit or Facebook. People in these communities often share and recommend good fanfics. You can post a request asking for Minato Kushina love fanfics, and you'll probably get some great suggestions from other fans.
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 good Minato Kushina fanfic could be 'The Love of Minato and Kushina'. It might focus on their relationship from the start, how they met, and the development of their love. It could show Minato's admiration for Kushina's strong will and Kushina's growing affection for Minato's kind heart.