Minato could be possessive of Naruto in fanfiction due to his guilt. He feels guilty for leaving Naruto alone in the world without his parents. This guilt might manifest as possessiveness, as he wants to protect Naruto from any harm and be the father he never got to be before. He wants to be the only one to guide and care for Naruto, thus showing possessive behavior.
In fanfiction, Minato's possessiveness of Naruto might also stem from his pride. Naruto is his son, and Minato was a great and powerful ninja. He sees so much potential in Naruto that he doesn't want others to influence Naruto in the wrong way. He wants Naruto to follow his ideals and values, and this desire to have Naruto be 'his' in terms of following his path can lead to possessive behavior.
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.
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.
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.
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.
In some Naruto fanfictions, Gaia might be possessive of Naruto because he represents a new hope or a different way of doing things. Gaia, being an important entity in the fanfiction universe, might see Naruto as a way to change the status quo. His kind - hearted nature and strong will could be what attracts her, and she's possessive to protect and guide him so that he can fulfill the potential she sees in him. She might also be possessive because she's the only one who truly understands his significance in the grand scheme of the fanfiction world.
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.
Sakura could be another main character. She might be shocked by Naruto's arrest and start her own investigation. Maybe she teams up with Sasuke, who also has his own complex feelings towards Naruto. Their combined efforts could play an important role in uncovering the truth.
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.