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.
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.
One characteristic is their similar determination. Minato was determined to protect the village at all costs, and Naruto has the same unwavering resolve. This determination drives them to keep pushing their limits and achieving great things.
It could be that Naruto is trying to prove himself. He wants to show that he can be as great a fighter as his father. Also, he might have received some training or knowledge transfer from someone who knew Minato well. This could have inspired him to adopt Minato's fighting style. He may also be in a situation where his normal fighting style isn't working, so he turns to Minato's as a last resort.
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.
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.
In the 'naruto is more like minato fanfiction', their relationship with the Nine - Tailed Fox could be similar. Minato sealed the Nine - Tails within Naruto. So, in fanfiction, Naruto might show a deeper connection to the Nine - Tails that is reminiscent of Minato's understanding and handling of the powerful beast. Maybe Naruto has an easier time controlling the Nine - Tails' power because he is more like Minato, as per the fanfiction. This could also tie into their overall power levels, as both being strong shinobi with a special relationship to the Nine - Tails.
Well, Naruto has some similarities to Minato. Physically, they both have blond hair. In terms of abilities, Naruto's speed and some of his jutsu - like the Rasengan which was passed down from Minato - show a connection. Also, their leadership qualities are alike. Naruto became the Hokage, just like Minato was, and they both had to lead their village in difficult times.
In the fanfiction, Naruto could show his genius in leadership, just like Minato. Minato was respected as a leader. Naruto may inspire others around him with his determination and positive attitude. He could come up with innovative plans to protect the village and its people, much like Minato did. Also, Naruto's ability to understand people's feelings and bring them together could be a sign of his genius in this aspect.
Naruto could incorporate Minato's sword - fighting skills if he has any in the fanfiction. Minato was known to be proficient with weapons. Also, Naruto might use Minato's strategy of quickly assessing the enemy's weaknesses and then striking precisely at those points. He could even use some of Minato's signature jutsu in a more efficient way, like the Rasengan, but with Minato's finesse.