Yes, there might be such fanfics out there. Fanfic writers often explore alternative storylines, and this would be a very dark and unexpected twist to the original Naruto story. It goes against the strong bond and rivalry that Naruto and Sasuke have in the canon, but that's the allure of fanfiction - to see what could happen if things took a drastically different turn.
In fanfictions about Naruto beating Sasuke in the Chunin Exams, the story could take a different turn for their relationship. Usually, Sasuke is the more skilled one in the early parts. But if Naruto wins, it could lead to Sasuke being more envious and determined to surpass Naruto in a different way. Naruto, feeling proud of his victory, might also be more motivated to keep getting stronger to maintain his edge over Sasuke.
In this fanfiction scenario, Naruto might be able to destroy Sasuke during the Chunin Exams due to his own growth and newfound abilities. Maybe he has mastered a new jutsu that gives him an edge over Sasuke. For example, if Naruto has fully harnessed the power of the Nine - Tails at this point, his strength could be overwhelming.
In many fanfictions about Naruto fighting Sasuke during the Chunin Exams, it often showcases their intense rivalry. One common aspect is the display of new jutsus that they might have developed secretly. For example, Naruto could have a new form of the Rasengan, and Sasuke might have evolved his Chidori in some unique way. This makes the fight more exciting as it goes beyond what we saw in the original series.
In such a fanfiction, the plot could involve Naruto being pushed to the extreme during the Chunin Exams. Maybe he witnesses some great injustice or threat to his friends that makes him cross his moral line and kill. For example, if an enemy tries to assassinate Sasuke during the exams and Naruto, in a fit of rage and desperation to protect his friend, uses a powerful jutsu that ends up killing the attacker.
He might kill an enemy shinobi from another village. For instance, if there is a particularly aggressive and cruel shinobi from the Sand Village during the Chunin Exams who poses a great threat to Naruto's friends or the Leaf Village in general, Naruto could be forced to kill him in self - defense or to protect others.
One reason could be if Sasuke was somehow possessed by a powerful and evil force during the Chunin Exams. Naruto might see no other way to stop this threat and be forced to kill Sasuke to protect the village and others. Another possibility is a huge misunderstanding. For example, if Sasuke was framed for a crime he didn't commit and Naruto was misled into believing he was a danger.
In this fanfic, Naruto and Sasuke might have an even more intense battle. Naruto could use his new jutsus that he learned from Jiraiya, like the Rasengan variations. Sasuke, on the other hand, might show off his improved Sharingan skills. Maybe he could even start to unlock some of the deeper powers of the Sharingan during the fight. And their fight could also attract the attention of other characters, like Sakura, who might be worried about Sasuke but also amazed by Naruto's growth.