One possible plot twist could be that when Harry travels back in time, he accidentally alters some other events which in turn create new challenges in saving Sirius. For example, he might change the location where Sirius is being held captive, or he could unknowingly alert the Death Eaters to his plan.
A really interesting plot twist could be that in the past, Sirius is actually in league with someone unexpected. When Harry travels back, he discovers that Sirius has made a deal with a character who is supposed to be on the side of good, but for some reason, they are keeping it a secret. This revelation would completely change Harry's perception of how to save Sirius and would add a whole new layer of complexity to the story.
It could be Kreacher. Normally seen as a rather unpleasant character, but in this fanfiction, he might have some hidden knowledge or ability that could prove crucial in saving Sirius. Maybe he knows some secret passages in the place where Sirius is held that no one else is aware of.
One possible plot twist could be that the marriage law is part of a dark plot. Maybe a powerful dark wizard has enacted it to create chaos. Harry and Sirius, instead of simply accepting it, start to investigate. They discover that the law is linked to an ancient prophecy that could bring either great good or great evil depending on how they handle their forced marriage situation.
A great plot twist could be the appearance of unexpected allies or enemies. Maybe Lupin, who is also an outcast in some ways, shows up and has a different view on how Sirius should raise Harry. On the enemy side, Voldemort's followers might figure out that Sirius has Harry and target them both. Also, Sirius could find out that there are some special powers within Harry that are being suppressed by the wizarding world's norms, and he has to fight to let Harry develop those powers.
One possible main plot twist could be that Sirius manages to completely hide Harry from the wizarding world's prying eyes until he comes of age. This would mean Harry grows up without the constant threat of Voldemort's followers finding him. Another twist could be that Sirius discovers some long - hidden magic within Harry that was dormant because of his upbringing with the Dursleys, but flourishes under Sirius's care.
It could be that when Harry saves Draco, a hidden prophecy is revealed. The prophecy states that their fates are intertwined and that they must work together to save the wizarding world from a greater evil that is yet to come. This forces them to put aside their differences and grudges and form an unlikely alliance.
One possible plot twist could be that Hermione discovers a hidden prophecy that only she can fulfill to save Snape. This prophecy might be related to some ancient magic that Snape has unknowingly become a part of. Another twist could be that in order to save Snape, Hermione has to team up with some of her former enemies, like Draco Malfoy, who also has a vested interest in Snape's survival for some reason. And perhaps the most unexpected twist could be that Snape's salvation is somehow linked to Hermione's ability to time - travel, which she uses to go back and change certain events that led to Snape's peril in the first place.
One interesting plot twist could be that when Harry travels back in time, he accidentally alters the events that led to Andromeda's relationship with the Black family. This could create a whole new set of family dynamics for her. For example, if Harry stops her from making a certain choice, it might lead to her being more involved with the dark side of the wizarding world initially, but then his presence in that time could also be the catalyst for her to change again and become a key figure in fighting against the dark forces in a different way than in the original timeline.
Perhaps Harry Potter travels back in time and ends up befriending a younger Bellatrix. He could try to influence her to not become a Death Eater. This would create a really complex situation because he has to balance not changing too much of the future while also trying to save her from the dark path. It could lead to some really intense moments where Harry has to hide his true identity and motives from her.
One possible plot twist could be that Sirius Black, being a wanted man, has to constantly move with Harry to avoid capture. This would make Harry's childhood very different from the one at the Dursleys. He'd grow up learning about the wizarding world on the run, perhaps meeting some unique characters in hiding places.
Perhaps the time travel is not what it seems. It could be a trap set by an unknown enemy. When Ichigo and Unohana think they are traveling through time to fix something, they are actually being led into a situation where they will be separated and used against each other. This would create a lot of drama and conflict in the fanfiction.