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.
A lot of Naruto fanfictions could be appealing to Team Minato. Fanfictions that show Team Minato's reaction to Naruto's friendship with Sasuke could be interesting. They might try to understand the complex bond between the two. Also, there are fanfictions where Team Minato discovers Naruto's hidden potential much earlier and helps him unlock it in ways different from the original story. This could lead to different storylines and character developments for Naruto and the whole Konoha village.
He could inherit Naruto's chakra - rich nature. So, he might have a large reserve of chakra like his father. Also, since Naruto has the Nine - Tails' chakra, Minato might have some sort of unique connection to it as well, perhaps being able to access a small portion of its power in a different way than Naruto does. And of course, he could inherit some of Naruto's signature jutsu like the Rasengan, but with his own twist.
One popular theme is time - travel. It often involves a character going back in time and changing the course of events in the Naruto universe. For example, a fanfiction might have Naruto traveling back to the time of the Fourth Hokage, Minato himself.
Even as a prodigy, Naruto might face challenges in the fanfiction. He could struggle with the high expectations placed on him. Since he's compared to Minato, people might expect him to perform at Minato's level all the time. This could put a lot of pressure on Naruto.
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.
Some people might write such fanfiction out of a desire for shock value. They think that by creating a completely different and controversial story, they can attract more attention. But this is a wrong approach as it distorts the original characters.
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.
The emotional bond would be stronger. Naruto wouldn't have to face the pain of growing up without a father. Minato could be there to cheer him on during his training and be a source of comfort when Naruto faced difficulties, like when he was bullied as a child. He could also help Naruto better control the Nine - Tails' power from the start.