One way this could be developed is if Naruto is somehow mind - controlled. For example, an enemy uses a powerful genjutsu on Naruto, making him lose his sense of self and see the Third Hokage as a threat to the village instead of a protector. Then, in his confused state, he attacks and kills the Third Hokage. This would create a huge moral and emotional conflict within the story, not only for Naruto when he comes to his senses but also for the entire village.
Perhaps in a dark fanfiction, Naruto discovers a dark secret about the Third Hokage that he believes makes him unworthy of leading. This secret could be something related to the Uchiha clan's massacre. Naruto, in his idealistic and sometimes headstrong way, decides to take matters into his own hands and challenges the Third Hokage to a fight, which ends in the Hokage's death. This would then lead to Naruto being seen as a villain by some and a hero by others who believe in his cause.
It could be a story where Naruto is tricked by a powerful antagonist. The antagonist convinces Naruto that the Third Hokage is planning to sacrifice him for the greater good of the village. Angry and feeling betrayed, Naruto attacks the Third Hokage without fully understanding the situation. After the killing, Naruto realizes he has been deceived, but it's too late. This sets off a chain of events where Naruto has to deal with the guilt and also face the consequences from the village.