There may exist. But it's not a common or well - received type of fanfiction. In the Naruto universe, Naruto is always trying to save his friends, especially Sasuke. And Sakura is also an important part of their team. The idea of Naruto killing them is so against the grain that it's likely only a very small niche of fanfiction writers would explore this concept.
There could be. Fanfiction allows for a wide range of interpretations and alternate storylines. But it's a really extreme and disturbing concept considering the bonds that Naruto, Sakura, and Sasuke share in the official story. It would be a very different take on the characters, and most fans who love the original story would probably find it hard to accept.
It's relatively rare. In the Naruto fandom, Naruto, Sasuke, and Sakura are central characters with complex relationships. Naruto and Sasuke are rivals but also friends, and Sakura is part of their team. Most fanfictions focus on their growth, friendship, or romantic relationships. Killing off two such important characters goes against the general positive and growth - oriented themes that many fans prefer.
One possible reason could be a sudden and extreme corruption of Naruto's character. Maybe he is influenced by some dark and powerful force that makes him turn against his friends. Another reason might be a misinterpretation of a prophecy or some kind of mind - control situation.
Perhaps in a fanfiction where the world has been completely turned upside down. If Sasuke had been tricked into becoming an unstoppable villain who was about to destroy the entire ninja world, and Sakura was somehow aiding him (maybe under a genjutsu), Naruto might feel he had no choice but to stop them by killing. Another reason could be a broken heart. If Naruto loved Sakura deeply but she constantly rejected him and chose Sasuke, and then Sasuke and Sakura betrayed him in some way, his anger and pain could lead to such a drastic act.
A possible motive could be a creative exploration of the 'what - if' scenarios. Maybe the writer wants to see how the story would unfold if Sasuke completely lost his way. Another motive could be to create a sense of high - stakes drama. Since Sakura is an important character, her death at Sasuke's hands would be a huge shock.
This fanfiction changes the power balance within Konoha. Sakura was growing to be a capable kunoichi. Her death would mean a loss of potential power and knowledge for Konoha. Also, it could lead to a rift between Sasuke and the village. Instead of being a potential ally or a wayward ninja, he becomes a murderer, and Konoha would have to deal with him differently.
I'm not sure if there is such a specific fanfic. The idea of Naruto killing Sasuke and Sakura goes against the general themes of friendship and redemption in the Naruto series. Most fanfics tend to explore positive relationships and character growth rather than such dark and out - of - character scenarios.
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.
One possible motive could be that Sakura is brainwashed. Maybe an enemy uses some kind of mind - control jutsu on her and she becomes a puppet to kill Sasuke. Another could be extreme jealousy. If she felt that Sasuke was slipping away from her in some way, in a very dark and twisted version of the story, it could lead to her killing him.
Maybe in a very dark and twisted fanfic, Naruto could be possessed by some evil force. This would override his normal sense of self and his love for his friends, causing him to harm them.
This type of fanfiction concept is really out of the ordinary. Naruto's character is built on his values of friendship, loyalty, and his dream of becoming Hokage. Killing Sasuke would mean betraying all of that. However, in a fanfiction, the author might be exploring the 'what - if' scenario. For example, what if Sasuke's actions against Konoha were so heinous that Naruto felt he had no choice? But still, it's a far - fetched and very different view from the original Naruto we know.