Maybe he realizes the exam is too dangerous or he discovers some unfairness in it. In the original Naruto story, Naruto has faced many difficulties and moral dilemmas during the Chunin Exam. So in the fanfiction, similar situations might push him to quit.
He might face disappointment from his friends and mentors. His friends who were also participating in the exam might feel let down, and his mentors, like Kakashi, could be concerned about his decision and how it will affect his future as a ninja.
Well, one thing that could happen is that Naruto, with his knowledge of future events, could easily ace the written part of the Chunin Exams. He might also be able to prevent some of the chaos that Orochimaru caused during the exams. For example, he could warn the proctors about Orochimaru's infiltration in advance.
One possible scenario in such a fanfic could be Naruto easily overpowering his opponents during the Chunin Exam. For example, in the written test, he might use some new, godlike power to read the minds of the examiners or sense the correct answers. During the combat rounds, he could defeat his foes with a single move, leaving everyone in awe. His newfound power might be related to some ancient ninja art he discovered or a special training he underwent secretly.
In this fanfiction scenario, Naruto and Yugito could have some really interesting interactions during the Chunin Exams. Maybe they start off as rivals, each determined to prove themselves in the exams. Naruto with his unwavering determination and Yugito with her unique skills. They might end up in a match against each other, and through the battle, they gain a newfound respect for one another's abilities.
One idea could be that Naruto forms an unexpected alliance with Anko during the Chunin Exams. Maybe they team up to uncover a hidden plot within the exams that threatens the safety of all the genin. Anko, with her experience, could help Naruto see things from a different perspective and he, in turn, could inspire her with his determination.
One idea could be that female Naruto has unique jutsu in the Chunin Exams. For example, she might have a more refined version of the Shadow Clone Jutsu, which surprises the opponents and judges. Her character could also show more emotional intelligence during the exams, like using her understanding of others' feelings to her advantage in battle, perhaps by predicting their moves based on their emotions.
There might be fanfictions that Chunin imports which are centered around relationships in the 'Naruto' world. This could be friendships that were not fully explored in the original, like the relationship between different clans' members. Or perhaps romantic relationships that add a new dimension to the story.