One interesting plot could be a character using the permanent Felix Felicis to solve a long - forgotten mystery in the wizarding world. For example, they might discover the true origin of an ancient spell that has been lost in time. Another could involve a student using it to always ace their exams and then getting into some trouble when the professors suspect foul play.
Hermione Granger is also a popular choice. Given her intelligence and love for learning about potions, it's easy to imagine her either creating more Felix Felicis or using it in a clever way to solve a problem at Hogwarts.
One idea could be a story where a student who is usually very unlucky gets ahold of Felix Felicis. They use it to turn their academic and social life around, but then face the challenge of whether their newfound success is truly theirs or just the result of the potion.
A really cool plot could be where the Permanent Felix Felicis has some unforeseen side - effects. Instead of just bringing good luck, it starts to warp reality in small ways. The main character has to figure out how to reverse or control these effects while also dealing with the regular challenges at Hogwarts like exams and rivalries. This would add an element of mystery and danger to the story, making it more exciting.
In many 'Harry Potter Permanent Felix Felicis Fanfiction', Ron Weasley could be one of the main characters. He often gets into all sorts of situations with Harry and Hermione, and with the addition of the permanent Felix Felicis, his character could have some really interesting developments. Additionally, some original characters created by the fanfiction authors might be main characters. These could be new students at Hogwarts who discover the permanent Felix Felicis and have to deal with the consequences.
Hermione Granger could also be a central figure. Given her intelligence and thirst for knowledge, she could be researching the Permanent Felix Felicis and its implications, and might accidentally consume it or use it in an experiment. She would then use her wits along with the potion's effects to navigate through various situations.
There's a fanfic called 'Harry Felix: The Bond'. In this one, their friendship is explored in depth. It shows how they support each other through various challenges, with detailed descriptions of their emotions and the world they live in. It's a really heartwarming read that fans of the 'Harry Felix' concept would enjoy.
You can try fanfic websites like Archive of Our Own (AO3). It has a large collection of fanfics from various fandoms, including 'Harry Felix' ones. Just search for the relevant tags.
One common theme is loyalty. Since they are mates, their loyalty to each other is often a central aspect. Another is adventure, as they might go on quests together.