In some fanfics, Snape may use a potion similar to the Felix Felicis, the luck potion. But instead of just bringing luck, this modified version could be used to change Harry's fate or the course of his actions. It could make Harry more inclined to make certain choices that Snape desires. Also, there could be a potion that can temporarily suppress Harry's magic, which Snape might use to keep Harry out of trouble or to protect him in a different way.
Maybe Snape wants to train Harry better. By using potions to change Harry's abilities or characteristics, he can expose Harry to different challenges and make him a stronger wizard. For instance, if he gives Harry a potion that temporarily takes away his ability to use magic, Harry will have to learn to rely on other skills.
Snape teaches Harry about potions in a rather strict and demanding way. He often criticizes Harry's mistakes harshly but also imparts important knowledge about potion - making techniques, ingredient properties, and the correct procedures to follow in the classroom.
Snape is likely to be initially suspicious. He has long held a rather negative view of Harry, so when he discovers Harry is good at potions, he might think Harry has some ulterior motives or has received improper help. After all, in the regular Hogwarts setting, their relationship is quite tense.
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.
Well, his potion skills might make Snape a bit more lenient towards him. Since Snape is the potions master, he might respect Harry's talent more, reducing the usual animosity. With his friends, Harry could share potion-making tips, strengthening their bond. For example, he could help Hermione with some tricky potion recipes, and she'd be impressed by his newfound skills.
I'm sorry I can't directly recommend a specific one off the top of my head. But like I said before, you should check out Fanfiction.net or Archive of Our Own. Just type in the relevant keywords and browse through the results. There are so many fanfics on these platforms that you're bound to find one that suits your taste.
Maybe Harry has had some secret interactions with Snape that the readers haven't known about yet. These interactions could have made Harry feel a father - like connection to Snape, and in the heat of the moment in potions class, he just blurts it out.
Severus Snape is another character who could be considered a potions genius in fanfic. In the official story, he was a master of potions. Fanfic writers might explore more of his early days as a potions prodigy or create scenarios where he imparts his deep knowledge of potions to other characters in unique ways.
Snape might be initially shocked. His face could turn pale and his eyes widen in disbelief. But then, a small glimmer of something like pride or warmth might flash across his face for a split second before he quickly composes himself and snaps at Harry to focus on the potion.
Well, Draco could be punished by Snape for being disrespectful in Potions class. Snape might order Draco to write a long essay on the history and significance of a particular potion. This would not only be a humiliation for Draco but also a chance for him to gain more knowledge about potions. And it would add an interesting dynamic to their relationship as Draco would be resentful at first but might end up learning something valuable.