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.
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.
Yes, there are quite a few. You can check out fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Harry is good at potions' in their search bars, and you'll likely find some interesting stories.
In a lot of these fanfictions, it could be that Harry has a secret mentor. This could be an old wizard who has been secretly guiding Harry in potions, away from the prying eyes of the Hogwarts staff. This mentor could have seen Harry's potential early on and decided to help him develop his skills in private. Another aspect could be that Harry's own determination and his need to prove himself in a different area other than Quidditch or fighting Voldemort drives him to secretly practice and become good at potions. Also, the idea that there are hidden aspects of magic within him, perhaps related to the founders of Hogwarts, that only manifest in his potions - making ability.
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.
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.
In some fanfictions, Harry might be good at potions because the author wants to give him a new skill set. It could be that they want to show his growth and development in a different area than in the original books. Maybe he has a secret mentor or he discovers a hidden talent within himself through some unique experiences in the fanfiction world.
Often, they show Harry being confident in the potions classroom, which is a contrast to his original somewhat - nervous self. He might also be more respected by Snape, or at least not constantly picked on.
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.