One possible scenario is that Naruto would gain a lot more knowledge about the village's history and politics. The Sandaime, being an experienced Hokage, could teach Naruto about the different clans in the village, their relationships, and how to manage them. Naruto might also learn more advanced jutsu more quickly, as the Sandaime could give him personal training. This could make Naruto a much stronger ninja at a younger age and perhaps change the course of some of the earlier story arcs.
His training would likely be intense. The Sandaime would probably start with the basics of chakra control, making Naruto practice things like tree - walking and water - walking until he perfects them. Then, he might move on to teaching Naruto more advanced ninjutsu, like some of the Hirashin no Jutsu variants that only a few in the village know.
One possible plot could be Naruto learning unique jutsu directly from the Sandaime. For example, he might be taught some long - forgotten sealing techniques that give him an edge in battles. Another plot could involve Naruto getting insights into the village's history and politics from the Sandaime, which helps him better understand his role in the village.
Naruto's relationship with the villagers would improve more rapidly. The Sandaime could help Naruto show the villagers his growth and potential in a more organized way. Naruto would also have a different relationship with the other ninja. He'd be seen as someone with a closer connection to the Hokage, so they might be more respectful or more likely to follow his lead. And his relationship with his own inner self would change too. He'd have more confidence knowing he's being trained by such an important figure.
Well, characters who had a rough start in the village due to Sandaime's decisions might be likely to support the bashing. For example, Naruto himself could be one. Given his difficult childhood with little support from the village at first, which some might blame on Sandaime, he could be portrayed as having negative feelings towards him in these fanfictions.
Naruto would probably be extremely hurt. He has always looked up to the Sandaime as a grandfather figure. So, he might initially go into a state of shock and disbelief.
In a fanfiction where the Sandaime survives the Chunin Exams, Konoha would be a very different place. His wisdom and experience are invaluable. He might be able to prevent some of the internal strife that occurred after his death. Naruto would probably grow even faster under his continued guidance. And the relationship between the different ninja clans might be more stable with his leadership still in place.
In a 'Naruto son of Sandaime' fanfiction, the story could center around the relationship between Naruto and the other clans in the village. As the son of the Sandaime, they might view him differently. Some clans could try to befriend him for political reasons, while others might be jealous or suspicious. Naruto would have to navigate these complex relationships while also dealing with his own growth as a ninja and his desire to be recognized for his own merits, not just because of his father.
Perhaps in the fanfiction, the Sandaime betrays Naruto by revealing his secrets to the wrong people. Like, he tells about Naruto's connection to the Nine - Tails in a way that endangers Naruto. It could be because the Sandaime is trying to protect the village at all costs, even if it means sacrificing Naruto's well - being and trust.
Well, Naruto might become extremely powerful. The Sandaime Hokage has a wealth of knowledge and skills. He could teach Naruto some very unique jutsu and also help him better understand the values of the village. Maybe Naruto would grow faster in terms of combat skills and leadership abilities.