One interesting plot could be Snape going back and trying to prevent the death of Lily. He might use his knowledge of the future to change certain events that led to her demise. Maybe he would try to expose Pettigrew earlier or find a way to make James Potter more cautious.
Bellatrix Lestrange could also be a character who interacts with Snape. If Snape goes back far enough, he might try to influence Bellatrix's path and keep her from becoming such a devoted Death Eater. This could have a major impact on Voldemort's power and the overall balance of the wizarding world.
Obviously, Severus Snape is the central character. He is the one who travels back in time, so all the actions and changes are centered around him. But other important characters often include Lily Evans. Since Snape had a deep connection with her, he might try to interact with her in different ways to change the past.
One interesting plotline could be Snape going back and trying to prevent the death of Lily Potter. He might use his knowledge of the future to change certain events that led to her demise.
It's popular because it gives Snape a chance to rewrite his story. He was such a complex and tragic character in the original series, and in these fanfictions, he can correct his mistakes or make different choices.
One possible plot twist could be that when Harry goes back, he discovers that Snape's situation is far more complex than he initially thought. Maybe Snape was involved in some secret mission that put him in danger, and Harry's interference actually endangers the entire wizarding world in unexpected ways. For example, Snape might be on the verge of uncovering a new dark magic plot that Harry's presence disrupts.
One possible plot twist could be that Snape, in his attempt to save Harry, accidentally changes the entire future of the wizarding world. For example, he might prevent Voldemort from ever rising to power in the first place, which would mean that all the relationships and events that we know from the original story would be completely different. Another plot twist could be that Snape discovers that saving Harry is not as straightforward as he thought. Maybe there are dark forces at work that are trying to stop him from changing the past, and he has to fight against them while also trying to protect Harry.
Snape's character development could take a very different turn. He may start to value life more, not just Harry's but also those around him. In the original, his focus was mainly on his own pain and his loyalty to Dumbledore. But going back in time, he realizes that every action he takes can have a huge impact on the future. This could lead to him becoming a more empathetic character. He might also become more of a hero in the eyes of others, which is a big change from his somewhat villainous reputation in the original story. He could start to see himself in a new light and strive to be a better person not just for Harry's sake but for the sake of the entire wizarding world.
One great 'Snape goes back' fanfiction is 'Back in Time'. In this story, Snape goes back to his Hogwarts days and tries to change certain events. It's really interesting as it shows his internal struggle with his past self.
She could meet her younger self. This would be an interesting encounter as she could offer advice and guidance to her younger version. Maybe she could help her younger self to be less afraid of her powers.