It could initially create more tension. Harry might be suspicious of Snape's motives, especially considering their generally strained relationship. He could start to wonder if Snape is up to something malicious.
It could be a plot device used by the author of the fanfiction. The touch might be used to create tension or an emotional moment between Snape and Harry. It could signify a turning point in their relationship, whether it's the start of a more positive understanding or the heightening of an existing conflict. For example, the touch could make Harry feel uncomfortable and lead to a confrontation later, or it could make him realize that Snape has a more complex side than he initially thought.
In a more dramatic scenario, during a battle at Hogwarts. Snape might find Harry injured and touch him gently to assess his condition. This could be a very poignant moment as Snape, who has always had a difficult relationship with Harry, is now showing a side of concern. It could also lead to a new level of respect between them.
This is completely inappropriate. Fanfiction should be about exploring characters in a way that is in line with basic human values. This kind of description goes against decency and respect, and it is not something that should be part of any fan - based creative writing.
In some fanfictions, 'finger' might be used in a scolding or pointing sense. Snape could be singling Harry out in class by pointing his finger at him accusingly, perhaps when Harry has done something that goes against the rules of the class or Hogwarts in general. This action is often used to show Snape's strict and often unfair treatment of Harry in the eyes of the young wizard.
One negative impact is that it spreads immoral and vulgar ideas. It can also make the original work's fan community look bad as it goes against the positive and creative nature that fanfiction should have.
Draco could be made to stand in the corner of the classroom during the entire potions class as a punishment. This would be a public humiliation for him, especially in front of his peers. It would also show Snape's no - nonsense attitude towards misbehavior.
Another reason could be that Snape suspects Harry of some secret knowledge or activity. In the complex world of fanfiction, there could be hidden plots where Harry is involved in something that Snape is trying to uncover. By fingering Harry in class, he's trying to rattle Harry and get him to reveal something, either through his words or his actions during the class.
One possible reason could be Snape's sense of duty to protect Hogwarts students in general. Even though he dislikes Harry, he might put aside personal feelings to ensure the safety of a student in a dangerous tournament like the Triwizard Tournament. Another reason could be Dumbledore's influence. Dumbledore trusts Snape and may have asked him to keep an eye on Harry during this event.
Another interpretation is that it's a way to create conflict. In fanfiction, this can add drama. Snape's actions towards Harry in class can be a source of tension that drives the plot forward, as Harry may strive to overcome Snape's challenges or find ways to get back at him.