I'm not sure specifically as there could be many interpretations. It might be about a situation where Harry has reached a point of apathy or detachment in the fan - created story.
Perhaps Harry is so devoted to the original canon of a story, like a book series or a movie franchise, that he dismisses fanfiction. Fanfiction can sometimes deviate a great deal from the original, and if Harry is a purist, he might not care for these reinterpretations. He might think that the original creators' vision should be the only one considered, and fanfiction is just a distraction from that.
I'm not entirely sure specifically what that particular 'harry just doesn't care fanfiction' is about without reading it. It could be a story where Harry has a nonchalant or apathetic attitude towards certain events, characters, or situations in the Harry Potter universe. Maybe he doesn't care about the latest wizarding drama or the actions of his friends or foes.
You could try searching on popular fanfiction websites like Archive of Our Own (AO3) or Fanfiction.net. Just type in the exact title 'harry just doesn't care fanfiction' in their search bars.
In some fanfictions, Percy's lack of care could be due to a change in his personality after a major event. For example, if he's been betrayed by someone close to him. He might feel that the world of demigods is not what he thought it was. So, he starts to distance himself and act as if he doesn't care about the things that used to matter to him, like protecting Camp Half - Blood or going on quests. This can add an interesting twist to the fanfiction's plot.
It could mean a fan - created fictional story where the character Harry has reached a point of no longer caring about something. Maybe he's been through a lot in the original story context and in this fanfic, he's just given up on caring about certain events, relationships, or goals.
It might also suggest that the Harry Potter franchise, in an official capacity, doesn't really take into account fanfic. The official Harry Potter universe has its own set of stories, lore, and development. Fanfic is a separate realm created by fans for their own enjoyment. So, it's like Harry Potter, representing the official brand, is indifferent to fanfic because it exists in a different sphere of creativity.
I think it's not that common. Most fanfictions tend to follow the general traits of the characters from the original books. Since Harry is known for his loyalty and care for his friends, a fanfiction where he doesn't care about anyone is quite the opposite. However, it could be an interesting concept for some authors who want to break the mold and create something new and thought - provoking.
One interesting aspect could be the unique interpretations of the Harry Potter universe's rules. Since Harry doesn't care about time travel in this fanfiction, it might lead to wild and unorthodox plot developments. For example, time - related magical artifacts could be used in ways that are completely different from the original series.