Well, perhaps Snape sets them to clean the potions classroom. Draco tries to boss Harry around at first, but Harry refuses to be pushed. As they clean, they accidentally knock over a vial that releases a magical mist. The mist makes them relive some of their worst memories involving each other. This forces them to understand each other's perspectives better and by the end of detention, there's a less hostile air between them.
In a Harry and Snape detention fanfiction, Harry might finally have a chance to understand Snape better. He could see that Snape's strictness is not just pure malice but perhaps a result of his complex past. Snape, on the other hand, could start to see Harry not just as James Potter's son, but as an individual with his own struggles. They might end up having a conversation about magic that neither expected, leading to a newfound respect for each other.
It could change in a more positive way. In detention, they might have to rely on each other to get through Snape's tasks. If they are made to work on a complex magical experiment, they would need to communicate. This communication could break down some of the barriers between them. Maybe they start to exchange a few friendly words outside of detention, slowly building a more amicable relationship.
Well, Harry could be forced to clean the Potions classroom during detention. Snape might make him scrub every cauldron by hand while muttering about how clumsy Gryffindors are. Harry might accidentally spill a potion ingredient, which makes Snape even angrier and gives him more tasks to do, like sorting out all the potion ingredients in the store cupboard.
Perhaps Snape gives them the talk about the importance of unity in the face of the dark forces that are always lurking. He could be using his own experiences to make them understand that they should put aside their differences for the greater good. For example, he might talk about how during the war, internal disputes among wizards only made it easier for Voldemort to gain power. By uniting, they could be a stronger force against any potential threats. Also, Snape might use this talk to make them realize that their personal grudges are petty compared to the bigger issues at hand.
One possible plot could be that Snape suspects Harry and Draco of being involved in some sort of dangerous or forbidden magic experiment. In his frustration and concern for their safety and the safety of the school, he decides to take a very strict approach. However, this would require a lot of character development and deviation from the original character traits to make it somewhat believable in the context of the Harry Potter universe.
Well, in a detention with Snape in a Harry Potter fanfic, Harry might be forced to clean out the Potions storeroom. Snape could use this time to lecture Harry about his lack of respect for Potions as a subject. Maybe he would also drop some hints about Harry's father, James, which could be both infuriating and enlightening for Harry.
Well, one possible plot could be that they all inherit season tickets to the Panthers from some wizarding family member. Harry is excited because he's never really been into a Muggle sport like this before. Draco is initially snobbish about it but then gets really into the team spirit. Snape, on the other hand, is only interested in the strategy aspect of the game. And throughout the story, their different perspectives on being Panthers fans cause some clashes and also some unexpected friendships to form.
One possible plot could be that Snape, seeing Draco's vulnerability after the fall of the Malfoy family in the wizarding war, decides to take him in. Snape would then have to deal with Draco's emotional baggage and his own complex feelings towards the boy. He might try to teach Draco a different set of values than what he was brought up with in the Malfoy household.
One interesting plot point could be the two rivals being forced to work together during detention. They might start to see each other in a different light. For example, they could discover they both have a passion for a certain subject like potions, which they didn't know before because of their rivalry. Another plot point might be the challenges they face during the detention tasks. It could be something magical and dangerous that they have to overcome together, which builds an unexpected bond between them.
One interesting scenario could be that during detention, Snape makes Harry clean all the potion bottles in the dungeon while lecturing him about the importance of precision in potions. Harry, in turn, discovers an old, forgotten potion recipe among the bottles and Snape is grudgingly impressed.