In some fanfictions, Harry might be punished by Snape and Draco when he tries to interfere in Slytherin house affairs. For example, if he questions Draco's leadership in a Slytherin - Gryffindor rivalry event. They could then force Harry to participate in a difficult and dangerous task like retrieving an item from the Forbidden Forest. This not only serves as a punishment but also as a way to put Harry in a vulnerable position. And in other cases, if Harry is overheard saying something disrespectful about Snape's teaching methods, Snape and Draco could give him a punishment of having to attend extra Potions lectures during his free time.
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.
Well, perhaps Harry is found out to be involved in some prank that targeted Slytherin students. Snape, being the head of Slytherin, and Draco, as a Slytherin student himself, would then punish Harry. They could make Harry write lines about the importance of respecting other houses, like 'I will not play pranks on Slytherin students' a hundred times. It's also possible that if Harry is caught using an unauthorized spell in the corridors near the Slytherin dormitory, Snape and Draco might take away his Quidditch privileges for a while as a punishment.
Snape could also assign Draco to do research on a particular dark magic item or spell. This would be a punishment as it would involve a lot of time and effort, and also expose Draco to the dangerous side of magic that Snape wants him to be cautious about. It also gives Draco a chance to learn more about the consequences of misusing magic.
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.
One common scenario is Snape protecting Draco from the other Death Eaters. Since Draco is young and somewhat naive in the ways of the Dark Arts and the Death Eater world, Snape steps in to keep him safe. Another scenario could be Snape helping Draco with his schoolwork, especially in Potions. Snape, being a master of Potions, would be able to guide Draco and boost his confidence in that subject.
One common scenario is in school settings. When other students are bullying Harry or trying to harm him, Draco steps in to protect. Another could be during dangerous magical events. For instance, when a dark magic spell is about to hit Harry, Draco uses his own magic to shield Harry.
One common scenario is when Draco is in trouble with other students, especially Gryffindors. Snape steps in and defends Draco, using his position as a teacher to put the other students in their place. For example, if Harry Potter and his friends are confronting Draco about something, Snape would quickly come to Draco's side.
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.
Often, Snape will single out Harry in front of the whole class. He might publicly criticize Harry's work or attitude. For example, when Harry is assigned a group project in Potions, Snape might give Harry extra tasks or set higher standards just for him. And during exams, Snape could be extra strict when grading Harry's papers.
One common scenario is that Snape saves Harry's life in a more personal way than in the original story. This act of heroism makes Harry see Snape in a new light and starts the journey towards friendship. Another is when they discover a common interest, like a love for a particular type of magic or potion - making. This shared interest bridges the gap between them.
Sometimes, in these fanfictions, the punishment is related to a competition. Say there's a magical tournament or a Quidditch - related event where Draco believes Harry has cheated or played unfairly. Draco, being the proud Slytherin he is, decides to punish Harry. It could involve making Harry do embarrassing tasks or even trying to get him banned from future competitions.
One common scenario is in a dangerous magical situation. For example, in a battle at Hogwarts, Draco might step in to protect Harry from a dark wizard's spell. Another could be in the face of social threats within the school. Maybe some students are trying to bully Harry, and Draco, having a change of heart, defends him. It could also be that Draco protects Harry from a plot within the Slytherin house that aims to harm Harry due to his fame as 'The Boy Who Lived'.