At first, Minato might be a bit confused and in awe of female Naruto. He would see her as this strong and powerful figure who has taken him in. As time goes on, he would start to trust her more and look up to her as a role model. Naruto, on the other hand, would be very protective of Minato and would want to ensure he grows up to be a great ninja.
Perhaps in this fan - made story, the world has been altered in such a way that Naruto is born as a female and she discovers Minato as an orphan. She decides to adopt him out of a sense of duty or a connection she feels to her own past. She would then raise him with her own set of values and ninja skills, which would be really interesting as Minato would be influenced by Naruto's different perspective.
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.
Minato could also teach Naruto about leadership. As the Fourth Hokage, he led Konoha. He could share his experiences on how to make tough decisions for the good of the village and its people. He might tell Naruto stories of past battles and how he strategized to win, which would help Naruto in his future as a leader in Konoha.
One common ability is their speed. Minato was known as the Yellow Flash for his incredible speed. Naruto, with his Sage Mode and later forms, can also move extremely fast. Another is their use of the Rasengan. Minato created the Rasengan, and Naruto has mastered it and even developed it further.