A common theme is family and clan loyalty. Since the Sarutobi are an important clan in the Naruto universe, many OC fanfictions explore how the original characters uphold the values and traditions of the clan. Another theme is the pursuit of power. OCs often strive to become strong ninjas, just like the well - known Sarutobi characters in the original series.
Perhaps in this fanfiction, Sarutobi is trapped in a genjutsu created by a rogue ninja. Naruto, being highly resistant to genjutsu due to his Uzumaki blood, manages to break into the genjutsu world. There, he has to fight his own inner demons as well as the rogue ninja's illusions to free Sarutobi.
Training and growth is also a frequent theme. The female OC might be shown going through rigorous ninja training, developing her skills, and facing challenges along the way. This often includes her learning from the more experienced Sarutobi members or surpassing their expectations.
One possible fanfiction could be about an OC (original character) who is a student of Hiruzen Sarutobi. This OC has always heard tales of Minato Namikaze's heroics. The story could involve the OC getting into a difficult situation, perhaps a dangerous mission, and drawing inspiration from the skills and courage of Minato. Hiruzen, as the wise teacher, could guide the OC in learning from Minato's example. For example, the OC might be struggling with a new jutsu, and Hiruzen tells them how Minato mastered a similar one with his determination and innovation.
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.
Perhaps he uses some ninja techniques like a shadow clone jutsu. He could make multiple clones to help him sort through and complete the paperwork quickly.
One great Sarutobi OC fanfiction is 'The Hidden Sarutobi'. It focuses on an original character within the Sarutobi clan who has unique abilities and has to face various challenges in the Naruto world. Another is 'Sarutobi's New Hope' which explores the story of an OC who befriends the Sarutobi family members and gets involved in important events in the village.
Naruto would probably be extremely hurt. He has always looked up to Sarutobi as a leader and a father figure. His first reaction might be disbelief, unable to accept that Sarutobi would do such a thing. Then he would likely feel a great sense of anger and betrayal. He might lash out and try to prove his innocence.