Snape could also punish Draco by deducting house points. Since Draco is in Slytherin, losing house points is a big blow to his pride and to the whole Slytherin house. This would make Draco the target of his housemates' ire, adding to the punishment's severity.
One common scenario could be that Harry is caught sneaking around the Slytherin common room or stealing potions ingredients from Snape's stores. So, Snape and Draco might make him do extra detention tasks like scrubbing the cauldrons for hours without magic. Another situation could be if Harry is suspected of cheating in a Potions exam. Draco might report it to Snape, and they could punish Harry by making him redo all his Potions experiments from the semester.
In fanfiction, Snape might punish Draco for getting involved with the wrong crowd. For example, if Draco starts to associate with Death Eaters - in - training or those with malicious intentions. Also, if Draco fails to complete his academic tasks or cheats in exams, Snape would surely take action. This is because Snape values knowledge and academic integrity in Hogwarts. Additionally, if Draco causes trouble during important school events or ceremonies, Snape would likely punish him to set an example for other students.
Harry's reaction can be complex. At first, he may show immediate resistance, arguing that he's been wrongly accused. When he realizes that arguing won't get him anywhere, he might become sullen and withdrawn. However, this sullenness is also a sign of his determination not to let them break his spirit. He'll keep thinking of ways to prove his innocence or to show that their punishment is unjust. In some fanfictions, Harry also uses these punishments as a motivation to become better at magic, so that he can one day stand up to Snape and Draco more effectively.
Another reason might be that Harry is suspected of sneaking around in areas where he's not supposed to be. Snape, as a vigilant teacher, may punish Harry to maintain discipline in the school. He may think Harry is up to something related to the ongoing dangerous situations in the wizarding world and wants to keep him in line.
Jealousy could be a big motive. Harry is often the center of attention, and Draco, who is used to being in the spotlight in his own Slytherin circle, might be jealous. So he punishes Harry to try and knock him down a peg or two.
In some fanfictions, Snape might punish Harry by giving him extra detention tasks like scrubbing the cauldrons in the Potions classroom until they shine. This is a common form of punishment as it's within Snape's domain as the Potions master.
In some fanfics, Snape might punish Harry because of his perceived insolence in class. Harry has a rebellious streak, and Snape, being strict, wouldn't tolerate any behavior that he deems disrespectful to his authority as a teacher.
One reason could be Draco's arrogance. If Draco shows too much pride and disrespect in class, Snape, who values discipline, would not tolerate it. For example, if Draco mocks other students' potions attempts, Snape might punish him.
One reason could be Harry's resemblance to his father. Snape had a long - standing grudge against James Potter, and seeing Harry might trigger those old feelings. In slash fanfiction, this can be exaggerated, with Snape being harsher on Harry because of his connection to James.