He might start to rely on his friends more. For example, Sasuke and Sakura could become his main source of emotional support. He would focus on training with them and sharing his feelings, which in turn helps him to grow stronger and more independent.
One reason could be that the focus in Minato fanfiction is often on Minato himself and his heroic deeds. Writers might forget that Naruto, as Minato's son, should also have a significant role. To fix it, writers could incorporate more of Naruto's feelings about his father. For example, Naruto could have internal dialogues about how he wishes he had known Minato better or how he tries to live up to his father's legacy.
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.
Naruto's character may develop a sense of independence. Since he was neglected by Minato, he has to rely on himself more. He becomes more self - reliant and less likely to depend on others for help.
One possible storyline could be Naruto growing up feeling isolated and constantly seeking validation. He might strive harder in his ninja training to prove himself, not just to the village but also to the memory of his father. Another could be that he forms stronger bonds with other outcasts in the village, like Rock Lee, who also had to overcome challenges.
In fanfiction, Naruto and Minato often represent a connection between generations. Minato was a great ninja in his time, and Naruto is following in his footsteps. Fanfictions can explore how Naruto lives up to his father's reputation.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide variety of themes and scenarios, some of which might be rather strange or controversial. However, Naruto fanfiction often explores different relationships and alternate storylines, but this particular one seems a bit unorthodox and I haven't personally come across it.
One popular theme is Minato getting to know Naruto in the afterlife. Since Minato died when Naruto was a baby, fanfictions often explore their relationship in a spiritual realm.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.
Minato would likely be extremely shocked. Naruto is his son, and the idea of Naruto attacking him would be completely unexpected. He would probably try to talk to Naruto first, to find out what is wrong and why he is being attacked.