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.
One possibility could be that the Sandaime Hokage finally takes a really tough stance against the various threats to the village. For example, he might not be so lenient with Orochimaru from the start. Instead of just trying to persuade him, he could actively work on destroying Orochimaru's plans before they fully form. This would change the whole dynamic of how things played out in the original story, as Orochimaru was a major source of problems for Konoha.
He would probably be more confident. Knowing he is the son of the Sandaime, he has a strong lineage behind him. This could make him more assertive in his actions and decisions. For example, he might not be as hesitant to take on leadership roles in missions.
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.
One possible plotline could be that Naruto discovers a hidden threat to Sandaime before anyone else. Maybe he stumbles upon a secret enemy's plan while on a mission. He then uses his unique skills, like his shadow clones, to outwit the enemy and save Sandaime at the last moment. For example, he could create a diversion with his clones while he sneaks up on the bad guys and disarms them.
In a Naruto fanfiction, Orochimaru could be paired with the Sandaime in a more complex way. Not just as an enemy, but perhaps in a story where the Sandaime tries to redeem Orochimaru. Another character would be Minato. Even though they were from different generations, they both had a connection to Konoha's leadership. You could write about how the Sandaime influenced Minato or vice versa. And Iruka could also be paired with the Sandaime. Iruka is a teacher, and the Sandaime was also very much involved in the education and growth of the shinobi in Konoha. So, a story about how the Sandaime and Iruka work together to improve the academy or deal with problem students could be really interesting.
In a 'naruto son of bellatrix fanfiction', perhaps Naruto has some of Bellatrix's wild and unpredictable nature. He could be on a journey to discover his true identity and how he came to be Bellatrix's son. This might lead him to explore the secrets of the wizarding world and his own ninja abilities in a new light.
Well, one possibility could be that Naruto inherits some of Gilgamesh's arrogance along with his power. Maybe he has a special ability to summon ancient Babylonian weapons. And he could use this in his battles in the Naruto world, like against the Akatsuki.
One possible plot could be that Naruto discovers his true heritage as the son of a princess from a hidden kingdom. He then has to deal with the politics and expectations of the royal family while still maintaining his ninja ways. Maybe he has to protect the kingdom from a new threat using his ninja skills.
In such a fanfiction, perhaps Naruto could be shunned by the village from the start. His 'devil' heritage might give him strange powers that he has to hide. He could struggle with self - identity, different from the Naruto in the original who is seen as a hero. Maybe he has to fight against the prejudice of the people who believe the devil's son can only bring destruction.