In this fanfic, the Potters could have faked their deaths all along. They come back to rescue Harry when they find out how horribly the Dursleys are treating him. They might bring some magical creatures with them to help. For example, a phoenix that can heal Harry if he has any injuries from the Dursleys. Then they take Harry with them on a magical journey to a hidden wizarding community where they can all be safe and happy.
Sirius Black could also be part of it. He was Harry's godfather. He might have escaped from Azkaban earlier in this fanfic. He teams up with the Potters to rescue Harry. He could be the one who scouts out the Dursleys' house before the actual rescue operation, using his skills as an Animagus to stay hidden.
In the fanfic, Snape might use his knowledge of the Dursleys' house layout. He may enter the house unnoticed, find Harry, and then use a Portkey to quickly get them both out of there. He could also have some sort of charm or potion that he uses to counter any magic the Dursleys might have used to keep Harry there, like a spell - breaking potion. And he may have planned the whole rescue very carefully, choosing a time when the Dursleys are least likely to notice, like in the middle of the night.
In this fanfic, Sirius could be tipped off that the Dursleys are planning to send Harry away to some even worse place. So he swoops in. They flee to a remote wizarding village. There, Harry meets other wizards and witches who are sympathetic to his cause. Sirius helps Harry train in combat magic, as he anticipates future battles. Harry also gets to explore his magical heritage more freely without the Dursleys' restrictions.
Well, perhaps Daphne somehow discovers Harry's awful situation at the Dursleys. She might use magic to break into the house secretly. Then she could use a spell to make the Dursleys forget about Harry so that she can take him away without a fuss.
It could be that a non - human magical being, like a centaur or a house - elf with a strong sense of justice, takes Harry from the Dursleys. They might see the abuse and neglect he endures and decide to act. This could lead to Harry having a completely different perspective on the magical world as he's exposed to aspects of it that are not typically part of a human - centric view.
In this kind of fanfic, perhaps Harry has finally had enough of the Dursleys' mistreatment. He might use his magic in a moment of rage. Maybe he starts by levitating Dudley to teach him a lesson after one too many taunts. Or he could use a spell to make Aunt Petunia's precious china smash, as a way of getting back at her for all the years of neglect and cruelty.
The plot twist could be related to Snape's true motives. He might be under an Unbreakable Vow to rescue Harry from the Dursleys. In the process, Harry realizes that Snape is not as bad as he seems. This could lead to a complete change in their relationship. Harry could start to trust Snape, and Snape, in turn, could teach Harry some unique magic that he has never learned before, which is crucial for the upcoming battle against Voldemort.
Perhaps in this fanfic, Severus doesn't just save Harry physically from the Dursleys. He also saves Harry from the emotional and psychological damage that the Dursleys have been inflicting on him. Severus, having his own traumatic past, might be able to relate to Harry on a deeper level and starts to mentor him in ways that Dumbledore never could. This could lead to a completely different Harry, more confident and less impulsive.
Hermione could be one to rescue Harry. She might have discovered some new spell or potion that allows her to bypass the protections around the Dursleys' house and get to Harry. Then she'd use her intelligence and quick thinking to get him out of there safely.
In fanfiction, when the Potters meet the Dursleys, there could be a lot of tension. The Potters are magical and the Dursleys are muggles who despise anything out of the ordinary. There might be arguments as the Potters try to understand why the Dursleys have been so cruel to Harry. Or perhaps there could be a moment of redemption for the Dursleys as they see the good in the Potters and realize their mistakes in treating Harry so badly.