One really good one I read had a detailed courtroom scene where Harry used some really clever magic to present evidence. It was on FanFiction.net. Another great one on Archive of Our Own had a unique take on how the wizarding world politics played into Sirius' trial.
Well, Sirius might face a series of challenges during the trial. He could be wrongly accused and have to fight hard to prove his innocence. Maybe his friends would come to his aid, bringing new evidence or testifying on his behalf.
Obviously, Sirius himself is the central figure. His friends like Harry, Hermione, and Ron could be involved. They might be in the courtroom, trying to support Sirius in any way they can. The Ministry of Magic officials would also be there, as they are the ones conducting the trial.
In such a fanfiction, perhaps Harry discovers some new evidence that was overlooked. He might find a witness who was too afraid to come forward before. Then he presents this evidence to the Ministry, forcing them to give Sirius a trial.
The fanfiction could start with Sirius being magically transported to a new, more just courtroom. Dumbledore could be secretly working behind the scenes to ensure a fair trial. The trial could be full of twists and turns. For example, the dementors that were involved in his original imprisonment might be called as witnesses, but Sirius could use his knowledge of their weaknesses to discredit them. And in the end, he is proven innocent, much to the joy of his supporters and the shock of his enemies.
There may be such fanfiction in some niche corners of the internet, but this goes against the original nature of the Harry Potter series and is also a rather strange and inappropriate concept. J.K. Rowling's original works don't have any such plotlines, and most official and mainstream interpretations stay true to the original characters' relationships and story arcs.
Yes, there might be such fanfiction out there in the vast world of fan - created works. However, this kind of story often takes a rather unorthodox and perhaps controversial approach to the characters. Fanfiction can cover a wide range of themes and interpretations, but this one is likely to be quite different from the typical Harry Potter stories we know.
Maybe Sirius gets help from some powerful wizards or witches who believe in his innocence. They might testify on his behalf in front of the wizarding authorities. Sirius also could show his strong emotional bond with Harry. He has always been there for Harry in spirit, and now he can be there physically to raise him, which convinces the authorities to give him custody.
Hermione would definitely be a great help. She's smart and resourceful, and could do a lot of research to find evidence. Also, Ron would be there, providing support and loyalty as always.
Some independent fanfiction blogs also host such stories. However, they can be a bit harder to find. You can start by searching for Harry Potter fanfiction blogs through search engines. When you find some, check if they have a search function on the blog itself and look for the 'harry gets sirius a trial' fanfiction there.