Yes, in many fanfictions, Naruto is often depicted as a huge fan of the Fourth Hokage. After all, the Fourth Hokage is his father. Naruto grows up idolizing the Fourth Hokage's heroic deeds and wishes to be like him.
In this fanfiction, the plot might involve Naruto being tricked by an evil force into believing that the Fourth Hokage has some dark secrets. So he decides to fight him. It could also be a scenario where Naruto enters a different dimension where the Fourth Hokage is being controlled by an outside power, and Naruto has to free him by fighting. And during the fight, Naruto discovers new things about his father and his own abilities.
One possible plot twist could be that Naruto has to face an unexpected enemy from the past of the Fourth Hokage. Maybe a hidden group that was against Minato's policies and now they see Naruto as a threat. Another could be that Naruto discovers a new jutsu that Minato was developing but never completed, which changes the power dynamics in the village.
It's really hard to say. The Fourth Hokage was incredibly powerful, with his Flying Thunder God Technique and all. But Naruto has the Nine - Tails' power and has grown a lot. If it was a fair fight, it might depend on who has the better strategy. The Fourth is more experienced in combat, but Naruto has that raw power. So it could go either way.
Another scenario could be during battles. Naruto might be inspired by the Fourth Hokage's battle strategies. He may think to himself, 'What would the Fourth Hokage do in this situation?' and then try to act accordingly. In some fanfictions, Naruto even visualizes the Fourth Hokage beside him, giving him advice during tough battles.
His relationship with Sasuke would be very different. Sasuke might see Naruto in a new light, perhaps with more respect as he's achieved the highest position in the village. Naruto would also have a different dynamic with Kakashi. He'd be more of an equal now, and Kakashi would have to adjust to Naruto being in a leadership role.
It could be that in this fanfiction, Naruto has been influenced by some false information about the Fourth Hokage. Some villains might have spread lies about the Fourth Hokage's actions, and Naruto, being young and naive in the story, believes those lies and thus starts to hate the Fourth Hokage.
The original Naruto story has a lot of themes about Naruto following in the Fourth Hokage's footsteps. However, in this fanfiction, with Naruto hating the Fourth Hokage, it goes against that theme and creates a whole new set of character motivations and plot directions. For example, Naruto might oppose things that the Fourth Hokage once stood for, which would be very different from the original where he tries to uphold the values of the village like the Fourth Hokage did.
Sasuke could also be a possibility for the 6th Hokage in the fanfic. He has grown stronger over the years and his unique perspective on the ninja world could bring new ideas to the leadership of the Hidden Leaf. He might start off as a controversial choice but prove himself through his actions in protecting the village and making tough decisions.
Sasuke could be an alternative. He has strong ninja skills and a deep understanding of the ninja world. His experiences have made him grow into a very capable person, and his Sharingan gives him an edge in combat and strategic planning.