I'm not aware of any official 'Naruto kills his sister' fanfiction. This goes against the general nature of Naruto's character who values family and friends. Fanfiction that involves such extreme and out - of - character scenarios might be very rare or non - existent in the mainstream Naruto fanfic community.
If such a fanfiction exists, one possible reason could be a mind - control situation. Maybe an enemy uses some powerful genjutsu to make Naruto believe his sister is a threat, causing him to kill her accidentally. Another reason could be a misinformation plot where Naruto is tricked into thinking his sister has committed some unforgivable crime against the village.
Most of the fandom would probably be horrified. Naruto is known for his positive values, and killing a family member is completely against that. There would likely be a lot of criticism towards the author of such a fanfic.
One possible motive could be jealousy. Maybe she was jealous of Naruto's growing power and popularity within the village. Another reason might be related to some dark family secret or a curse that forces her to take his life against her will.
At first, Sasuke might not believe it was Naruto's own will. He would try to find out if Naruto was under some sort of external influence. But if he found out that Naruto was fully responsible, Sasuke's reaction would be one of pure hatred. He would abandon all his previous beliefs and goals and make it his sole mission to destroy Naruto. He might also cut off all ties with the village that Naruto was protecting, seeing it as an accomplice in his sister's death.
It could be an original character created just for the fanfiction. Many fanfiction writers like to introduce new characters to add their own unique twists to the story.
Well, 'naruto kills fanfiction' might be a really unique and out - there concept. It could be a satirical take on the Naruto fandom. Maybe it's about Naruto as a character being fed up with all the crazy and often inaccurate fanfiction written about him and decides to 'kill' it in a metaphorical way, like by changing the narrative or somehow stopping the spread of these fan - made stories.
I'm not sure if there is an actual 'naruto kills his sister fanfic' specifically. But if there were, it would be a very twisted take on the Naruto universe. Naruto has always been shown to value family, even if he didn't have a traditional family growing up. He found family in his friends and in the village. So this idea of him killing his sister would be a radical departure from his core values.
One possible plotline could be that Naruto is under some sort of dark magic or mind control. Maybe an enemy has found a way to manipulate his actions and make him turn on his friends. Another could be a situation where Naruto is tricked into believing his friends are actually enemies in disguise. For example, if there was a powerful genjutsu that made him see his friends as threats to the village.
There could be a 'naruto kills jiraiya fanfiction'. It could be based on a time - travel scenario. For example, if Naruto from the future travels back in time and somehow his actions cause a chain of events that lead to Jiraiya's death. Or perhaps there's a dark, alternate universe where Naruto's values are twisted and he sees Jiraiya as an obstacle to his new, malevolent goals and thus kills him.
I'm not sure if there is such a specific fanfiction. Fanfiction varies greatly in content and themes, and while it's possible for someone to create such a dark and out - of - the - ordinary plot in the Naruto fanfiction universe, I haven't come across it personally.