There are some fanfictions like this out there. One possible reason for such a plot could be exploring the 'what - ifs' in a very extreme way. Maybe the author wants to show how far a character can be pushed from their normal state. It could also be a way to explore the consequences of a broken mind or a character being corrupted by external forces. But it's a really sad and hard - to - accept concept considering the love and bond between Harry and Sirius in the original story.
In this type of fanfiction, the author may be trying to create a shock factor. Harry killing Sirius could be set in a parallel universe where everything is distorted. For example, Voldemort could have won earlier and manipulated Harry's mind to turn against his loved ones. Or there could be a new, extremely powerful dark magic artifact that makes Harry lose his sense of self and attack Sirius. But it's important to note that this is a very different take from the original, positive and hopeful tone of the Harry Potter series.
Yes, there might be some fanfiction with such a dark and alternate storyline. However, this goes completely against the essence of their relationship in the original series. In the canon, Sirius is a very important figure in Harry's life, like a father figure. So in this kind of fanfiction, it could be part of a dark magic - influenced scenario, perhaps Harry being under the Imperius Curse and forced to do it, or some extremely warped perception of reality that makes him think Sirius is a threat.
In such a fanfiction, it could be that Harry Potter has been corrupted by a powerful and malevolent force. This force might have warped his sense of right and wrong. It could also be that the author wants to explore the extreme consequences of power and how it can turn a hero into a villain. For example, if Harry Potter was constantly taunted and mistreated by the wizarding community despite all he has done, he might reach a breaking point and lash out at everyone.
Well, perhaps in a fanfic, Malfoy could be involved in a plot to destroy Hogwarts and Harry, in a fit of rage and desperation to protect his school and friends, ends up killing Malfoy. Or it could be that Malfoy is working with a new, extremely dangerous dark force, and Harry's attempts to stop him go too far and result in Malfoy's death. There could also be a scenario where Malfoy accidentally gets caught in the crossfire of a battle between Harry and another dark entity, and Harry is blamed for his death.
Maybe the goblins in the fanfiction have turned evil and are causing great harm to the wizarding world. Harry, seeing no other option, decides to take matters into his own hands and kill them to protect others.
In a more complex scenario, Bellatrix could be trying to use a dark magic ritual that would cause great harm to the wizarding world. Harry discovers her plan and has to engage her in a magical struggle. In the process, he manages to turn her own dark magic against her, which results in her death. This would show Harry's ingenuity and his ability to use the enemy's own weapons against them.
Well, perhaps Pettigrew gets tired of living in fear under Voldemort. He might find a powerful magical artifact that has the potential to kill Voldemort. As he tries to steal it for himself, Voldemort discovers his plan. In the ensuing struggle, Pettigrew manages to turn the artifact against Voldemort and kills him. This would then lead to Pettigrew having to deal with the consequences, like facing the wrath of the Death Eaters who are still loyal to Voldemort.
One possible reason could be a misunderstanding. Maybe some false information was spread about Harry that made Sirius believe he had done something unforgivable. For example, if there were rumors that Harry was involved with dark magic in some way, Sirius, who has a strong aversion to the dark side, might be quick to disown him.
Well, perhaps Sirius trains Harry in advanced defensive magic. Harry could learn spells like the Patronus charm more effectively under Sirius's tutelage. Sirius might also teach Harry about the wizarding world's secrets that Dumbledore didn't share.
One possible motive could be that the 'mountain' in the fanfiction represents a great evil or obstacle that is threatening the wizarding world. Harry, being the hero, feels it's his duty to eliminate it. For example, if the mountain is a lair for dark creatures that are attacking Hogwarts students.
One possible motive could be a misunderstanding. Maybe Snape is framed for something really bad, like a dark magic plot against Hogwarts. Harry, in his haste to protect the school and his friends, believes Snape is guilty and takes drastic action. Another reason could be if Snape accidentally endangers someone Harry loves dearly, like Ginny or Ron, and Harry's emotions get the better of him in the heat of the moment.
One possible motive could be a dark magic influence. Maybe some powerful dark wizard or dark artifact has corrupted Harry's mind, making him do something completely out of character like killing Cedric. For example, the Imperius Curse in a more insidious form that even Harry is not fully aware of could be at play.