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.
The best ones often explore the relationships between characters deeply. In some of these fanfictions, Harry's friendship with Hermione and Ron is shown as a crucial factor in getting Sirius a trial. They use their combined skills and knowledge to fight for Sirius. For example, Hermione's research skills and Ron's loyalty play important roles. There are also those that delve into the emotional aspect of Sirius being wrongly accused all those years and Harry's determination to right the wrong, which makes for a very engaging read.
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.
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.
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.
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.
One common theme is friendship. Sirius often uses his friendship with Harry as a starting point. He knows Harry well and wants to see him happy, so he uses that knowledge to bring Harry and Ginny closer. Another theme is the power of the past. Sirius, being from an older generation, has a different perspective on relationships. His influence from the past helps shape the relationship between Harry and Ginny in the present.
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.
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.
The fanfiction 'Harry and Sirius: A True Connection' is really good. It delves into how they build a deep emotional connection, like a father - son relationship. It's completely clean and focuses on things like Sirius teaching Harry about his family history and helping him deal with the challenges at Hogwarts. Another one is 'Sirius and Harry: Friendship and Beyond' which shows their friendship evolving in a very positive and appropriate manner. It has some really heart - warming scenes of them sharing stories and supporting each other.
One major problem is that it goes against the nature of the relationship between Sirius and Harry in the original 'Harry Potter' series. Their relationship is more of a mentor - mentee or a father - son like bond, not a romantic or sexual one.
One good Harry Sirius Potter fanfiction is 'The Bond Beyond Blood'. It explores the unique relationship between Harry and Sirius in a very heart - warming way. It shows how Sirius could have been more involved in Harry's life at Hogwarts if not for certain circumstances.