Well, it could be that Snape has been secretly keeping an eye on Harry all along. In the fanfiction world, he might have developed a new spell or potion specifically designed to counter the effects of Dementors. When he sees Harry in danger, he uses this new creation to save him. For example, he could have a potion that creates a protective shield around Harry, preventing the Dementors from getting close enough to suck out his soul.
In certain fanfictions, Snape's save could be more complex. It might be related to his past and his relationship with Harry's mother, Lily. His love for Lily, in a way, gives him the extra motivation and power. He could draw on some old magic that was once connected to Lily. He might sacrifice some of his own energy or magic to create a powerful Patronus that not only scares away the Dementors but also restores Harry's spirit if it has been affected by the Dementors' presence.
One reason could be his sense of duty. Despite his dislike for Harry on the surface, he might still feel responsible for the safety of all students at Hogwarts, including Harry. So when he sees Harry in danger from Dementors, he steps in to save him.
Another possibility is that Snape uses his position as a teacher. He might threaten Lockhart with the consequences of harming a student. Given Snape's intimidating presence and his own power within the school, Lockhart would be afraid to cross him. Snape could also call for other teachers to help, making it clear that he won't let Lockhart get away with any harm to Harry.
In this type of fanfiction, Snape could simply intimidate Vernon. Snape has an air of mystery and a certain power about him. He might show up at Vernon's doorstep, give Vernon a cold stare, and with his reputation as a powerful wizard, Vernon might be too scared to oppose him. Snape could then just take Harry without much resistance from Vernon.
Well, in some fanfictions, Snape might use his powerful magic skills secretly. He could cast a spell to deflect Bellatrix's attack aimed at Hermione just in time. For example, he might use a Protego spell in a very sneaky way that Bellatrix doesn't notice until it's too late.
It could also be due to his own inner strength and growth as a wizard. Harry has faced so many challenges and traumas throughout his life. His experiences might have awakened a latent power within him that allows him to control dementors. His strong willpower and determination, which have been developed over years of fighting against the dark forces, could be the key factor in this newfound ability.
Well, in some fanfictions, Harry might use a super - powered Patronus. His Patronus could be stronger than usual, perhaps due to some newfound magic or a special connection he has developed. It could be so powerful that it simply overpowers the dementors and destroys them.
Well, perhaps Snape could use his authority as a teacher. He might see Ron being too pushy or possessive towards Harry in a romantic sense and intervene by giving Ron extra assignments or detentions to keep him away from Harry.
In this fan fiction scenario, Snape might use his knowledge of the Muggle world and Vernon's weaknesses. Snape could have found out some information about Vernon's business affairs or personal secrets. Then he blackmails Vernon into leaving Harry alone. By doing this, he effectively saves Harry from Vernon without having to use too much magic and draw unwanted attention.
Well, it could change the plot in many ways. For example, he might be able to negotiate with them. Maybe he can convince them not to attack people, which would make Hogwarts a much safer place. He could also learn more about their origin and motives directly from them, instead of just speculating as others do.
Well, he might use his magic skills. Maybe he creates some protective spells around Harry to keep the werewolf at bay. For example, a strong shielding charm that can withstand the werewolf's attacks.