One possible plot could be that Naruto learns new jutsu from Asuma. Asuma might teach Naruto his unique wind - style jutsu, which could enhance Naruto's combat abilities. Naruto could also learn about leadership and strategy from Asuma, as Asuma was a respected leader in the Hidden Leaf. This training could make Naruto a more well - rounded shinobi.
I really like 'Naruto, Sasuke and Sarutobi: A New Beginning'. In this fanfic, it starts with Sarutobi having a premonition about the future of Naruto and Sasuke. So he takes steps to guide them differently. It's an interesting take on their relationship. 'Sasuke's Redemption under Sarutobi' is also good. It shows Sasuke trying to make amends with the village with Sarutobi's guiding spirit in mind. And 'The Hidden Power of the Trio' is a fanfic that gives a new perspective on the powers they possess and how they can be combined for the greater good.
In this type of fanfiction, it's possible that the story delves into Naruto's backstory and how being Sarutobi's son would have affected his childhood. Maybe he would have grown up with more guidance and support, which could have changed his personality. Instead of being the lonely outcast that he was in the original story, he could have been more confident from the start. The fanfiction might also introduce new characters related to Sarutobi that play important roles in Naruto's life. There could be new adventures and challenges that are unique to this new family dynamic, such as Naruto having to uphold the Sarutobi family name and legacy within the Hidden Leaf Village.
His relationship with the Leaf Village would become more personal. He'd be part of the Sarutobi clan in a sense. His bond with Shikamaru and Choji would strengthen as they are Asuma's students. Naruto would also have a new father - figure relationship, which would change how he views authority.
Well, it could be a story full of mentorship. Asuma could teach Naruto his unique jutsu, like the Wind Style. Naruto would also learn about Asuma's values, such as loyalty and perseverance. And perhaps they would bond over a shared love for food. Maybe Naruto would become closer to the Sarutobi family in general.
One great Anbu Naruto Sarutobi fanfiction is 'The Anbu's Hidden Mission'. It delves deep into Sarutobi's leadership within the Anbu and Naruto's unexpected role in a secret operation. The story is filled with intense action scenes and a touch of mystery.
Obviously, Naruto would be one of the main characters. And since it's about him being the son of Sarutobi, Sarutobi himself would be a crucial character. There would also likely be the usual Naruto characters like Sasuke, Sakura, Kakashi etc. as they would still be part of Naruto's life in the fanfiction, even with this new family relationship.
Naruto's character would become more mellow. Kurenai's gentle and nurturing nature would have a calming effect on him. He would be less impulsive. And with Asuma as a role model, Naruto would become more responsible. He would learn the importance of family and loyalty from them.
One possible storyline is a tournament - style arc. They enter a shinobi tournament as a team. Each member showcases their skills in different matches. Naruto might face a tough opponent with his Rasengan, Ino could use her mind - control in a strategic way against a female opponent, Kiba and Akamaru could have an exciting battle against a team with a similar animal - partner style, and Asuma could have a showdown with an old rival.
One idea could be a time - travel fanfic where Sarutobi goes back in time and tries to prevent the rift between Naruto and Sasuke from ever happening. Another could be a fanfic where Naruto and Sasuke are transported to a parallel universe where Sarutobi is still alive and they have to work with him to get back home. Or a fanfic where Sarutobi trains Naruto and Sasuke together in a secret art that no one else in the village knows about.