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.
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.
Obviously, Sirius Black himself is a key character. He's the one on trial, so he'll be at the center of the story. Then there's Harry Potter. He might be very involved, trying to prove Sirius's innocence. Hermione Granger could also be important, using her research skills to dig up evidence. And Remus Lupin, as Sirius's old friend, would be a crucial witness.
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.
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.
Sirius has to figure out how to give Harry a normal childhood while also training him in magic. He can't just let Harry be unprepared for the wizarding world, but he also doesn't want to push him too hard. Also, he may face financial difficulties. Raising a child isn't cheap, and he might have to find ways to earn money while also taking care of Harry.
There's also a fanfic where Sirius, after his death, somehow still manages to influence events. His spirit gives hints to Hermione, who then takes it upon herself to get Harry and Ginny together. This one has a really interesting take on how the afterlife can still have an impact on the living in the wizarding world.
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.
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.
One common theme is injustice. Since Sirius was wrongly accused, fanfictions often explore how unfair the trial was. Another theme is loyalty, as his friends' loyalty to him is shown in different ways. For example, they might try to find evidence to clear his name.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide range of themes and ideas, but this one seems rather unusual. You could try searching on popular fanfiction websites like Archive of Our Own or FanFiction.net to see if it exists.