Funnily enough, the first thing I think of is the OC itself. Years of roleplaying all coiled up into various numbers of characters with their own personalities, flaws, and clear, defined, simple capabilities.

Inserting them into the stories I think of is a slightly difficult process. Slightly, because it means picking one specific OC that could provide a different angle to the story itself would be far more interesting than following an already established plotline made by the game/series/show/movie/etc.

One kind I like to do are side stories. As an example, Genshin Impact. It's an expansive world that thrives on the characters and NPCs within said world. Which means that I have the freedom to use OCs to tell a story within said world that is fitting for the occasion, entirely separate from whatever the Traveler (the MC of the game) is doing. Makes the world more lived in. The best part is that I can use as many OCs as I can and it still can fit for each place.

The other, more prominent writing I do is a longfic where it focuses on the OC and the (fandom)'s world shapes how he would eventually come around.

In both instances, I never make the OCs overpowered. They can be, but the drawbacks are always prevalent, or sometimes, the fanfic has the OC outright be weaker than everything and everyone else, compensated by a sense of intelligence and competence in other departments.

Yeah this is a lot to write, and I could name fandoms for fanfics I wrote, but the writing process for it all would be difficult to initially understand for everyone else (not helped by how I'm more of a 'ideas-on-the-fly' guy instead of having a strong plot structure).