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.
There is a fanfiction where Harry discovers he has a natural aptitude for potions because of some ancient magic in his bloodline. It's called 'Potions Master Harry'. In it, he starts to experiment with potions in ways no one has thought of before, creating new and powerful elixirs. This not only changes his relationship with his classmates but also makes him a target for some dark forces who want to use his skills for their own evil purposes.
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.
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.
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.
One common plotline is that Harry's potion - making skills earn him a special place in Snape's class. For example, he might discover a new potion ingredient or brewing method that no one else knew. Another is that his skills lead to him getting involved in some sort of secret or mystery related to potions, like an old potion recipe that holds a key to a hidden treasure.
One possibility could be a story where Harry discovers a rare potion recipe and masters it, using it to solve difficult problems at Hogwarts.
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.
Snape could react in different ways. He might be even harsher, thinking Harry is being weak. Or, on the rare occasion, he could show a bit of understanding, which would be a huge change in their relationship. This could potentially change the whole dynamic in future potions classes.
It could be that he has a bad accident in the potions lab. For example, a potion explodes and nearly kills him or one of his friends. This traumatic experience makes him lose his confidence and interest in potions, leading him to quit as seen in some fanfictions.
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.