Yes, there are such fanfictions in the Naruto fanfiction community. Some fans like to explore unique and creative scenarios in their writing, including this rather unexpected one.
It might be for Naruto's own good. Sasuke may believe that Naruto is on a dangerous path that will lead to his downfall. So he captures him to keep him from making bad decisions, like sacrificing himself for the village or something similar. He wants to save Naruto from himself in a sense.
In some fanfictions, Naruto might reject Sasuke because of Sasuke's continuous pursuit of power in a way that endangers others. Naruto, who values friendship and the safety of the village, could see this as a betrayal of their shared values.
Naruto might protect Sasuke by using his physical strength. He's got those powerful jutsus like the Rasengan. If any enemy comes near Sasuke, Naruto can just blast them away with his attacks.
One popular type of fanfiction could be about their friendship. For example, a story might focus on a mission where Sasuke, Sakura and Naruto have to work together in a really difficult situation. They could use their individual skills, Naruto's brute strength and positive attitude, Sasuke's cool-headedness and powerful jutsu, and Sakura's medical knowledge and combat skills to overcome the odds.
The 'naruto rejects sasuke fanfiction' alters their relationship drastically. It takes away the hope of reconciliation that is often present in the original story. Naruto's rejection could push Sasuke further into his dark path, making him more bitter and vengeful. For Naruto, it's a difficult decision that might haunt him, but he feels it's necessary. This new state of their relationship means they no longer have each other's backs. Their connection, which was once so strong, is now broken, and they are likely to be on opposing sides in any future encounters.
In such a fanfiction, it could lead to a completely different power dynamic within the ninja village. Maybe Naruto's absence would give rise to new challenges and characters stepping up.
Normal fanfiction usually focuses on elements like their friendship, rivalry, or their roles in the Naruto universe. For example, it might explore how they influence each other's growth as ninjas. However, 'Naruto x Sasuke hard lemon fanfiction' often contains inappropriate and adult - themed content that is not in line with the general spirit of the Naruto series.
If Sasuke's sister was in the picture, Naruto and Sasuke's relationship might soften more quickly. Naruto would see another side of Sasuke through his sister. He might also feel more of a connection to Sasuke's family. Sasuke, on the other hand, would see Naruto's genuine care for his sister, which could make him trust Naruto more.