Well, it could start with Naruto being in a situation where he feels lost about his own path. Then, he starts researching about Minato more deeply. He finds out about Minato's early struggles, how he overcame them, and his great contributions to Konoha. As Naruto delves into Minato's story, he realizes that Minato was a true hero in every sense. This realization makes Naruto look up to Minato, and he decides to incorporate Minato's values into his own ninja way.
Naruto's relationship with the villagers could be affected. As he becomes a Minato fan, he would try to uphold Minato's legacy even more. The villagers, seeing Naruto's newfound admiration for Minato, might start to see Naruto in a new light, more like how they saw Minato. Also, his relationship with Hinata could be different. Naruto might start to model his family - centered values after Minato, which could bring him and Hinata even closer as they plan their own family.
Naruto might become more calm. Minato was a very composed person, and if Naruto becomes like him, he'll lose some of his impulsive nature. For example, instead of rushing into battle head - first all the time, he'll start to think more strategically like Minato did.
Another aspect could be in Naruto's leadership. As he grows older, he realizes the importance of Minato's calm and collected leadership in Konoha. Naruto might start to mimic Minato's diplomatic approach when dealing with other villages, just as Minato was respected for his ability to maintain peace and alliances. He could learn from Minato's past actions and start to handle village politics and international relations in a more Minato - like way.
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.
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 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.
You can try websites like Fanfiction.net or Archive of Our Own (AO3). They have a vast collection of Naruto fanfictions. Just search for 'Minato' and 'Naruto' in the search bar, and you'll get a list of relevant stories.
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.