Yes, there are quite a few. You can check out fanfiction websites like Archive of Our Own. Just search for 'Harry likes potions' and you'll find a variety of stories with different plotlines and writing styles.
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.
Maybe he was poisoned. There could be someone who slipped a harmful potion ingredient into his cauldron without him noticing. It's a common plot device in fanfics to create drama.
It could be Malfoy. He often has a vendetta against Harry and might have found a way to make him collapse during potions class, either by tampering with his ingredients or distracting him in a way that leads to a mistake in the potion - making process.
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.
One scenario could be a potions - making competition against a rival from another wizarding school. The rival might be known for their potions skills too, and Harry has to prove himself. Another situation could be when a dangerous illness spreads in Hogwarts, and Harry has to quickly brew a complex healing potion to save his classmates. Or perhaps a dark wizard challenges Harry to a potions duel, where they have to create potions with specific effects under pressure.
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.
A deep understanding of ingredients is crucial. They need to know not just what each ingredient does, but also how different ingredients interact with each other. For example, knowing that adding a sprig of dittany at a precise moment can change the entire nature of a potion.
One possibility is that a potions accident could cause a time - related mishap. Maybe the potion was supposed to be a simple Sleeping Draught but due to the accident, it creates a time - loop. The characters find themselves repeating the same day over and over until they figure out how to reverse the effects of the botched potion. This could be a really interesting plot device in a Harry Potter fanfic as it would allow for a lot of character development and exploration of different choices within the same day.