It could also be a result of some ancient magic that Percy stumbles upon during one of his adventures. For example, he might find an old artifact that imbues him with the power to control fire. And this new power would then be something he has to learn to master, which could lead to all sorts of interesting storylines as he tries to balance it with his existing powers.
Perhaps Percy has some long - lost heritage related to a fire - based creature or being. This could be something that is only revealed in the fanfic. His fire - controlling ability might be an inborn trait that has been dormant until a certain event triggers it. It could be a major plot point in the fanfic, as Percy has to come to terms with this new part of his identity while still being the hero we all know from the original books.
One way could be that it's a gift from a minor god. Maybe a god associated with fire secretly blessed Percy, giving him this power.
There are quite a few Percy Jackson fanfics where he controls fire. You can start by looking on fanfiction.net or Archive of Our Own. Try searching for 'Percy Jackson fire control' in the search bars of these platforms.
Well, in some fanfictions, Percy might start playing the piano as a way to relax. Maybe he discovers his talent when he stumbles upon an old piano in a hidden part of Camp Half - Blood. His demi - god abilities could give him an edge in learning quickly, like he has an intuitive understanding of the music. He could also be inspired by the stories and emotions around him at the camp, which he then expresses through his piano playing.
Percy's time - controlling ability might add a lot of twists to the plot. If he can control time, he could potentially stop time to outwit his enemies. This would make battles much easier for him and his friends. Also, he could use it to relive certain moments to gain more information. For instance, if there was a mystery about an event in the past, he could go back and observe it closely, which would then drive the plot forward as he uses the new knowledge to solve current problems.
Well, sometimes in fanfiction, his brother might be a mortal who discovers his demigod heritage later. This could add an interesting twist to the story as he has to adapt to the world of gods and monsters. Or it could be a long - lost half - brother from a different camp, like a son of Poseidon from another part of the world who was hidden away for some reason.
Well, take the 'Quest Log' ability. In Percy Jackson, quests are a huge part of the story. An OC with a 'Quest Log' ability can have a mental or physical log that details the steps and requirements of a quest, just like in a game. It can show them the main objective, side quests, and even give hints on how to complete them. This fits into the mythology as quests are often complex and having such an ability would make the OC more efficient in fulfilling their tasks.
Percy could start to form new relationships within the Faunus community. These relationships could teach him different values and ways of life. Maybe he'd meet a Faunus mentor who would help him understand and control his new Faunus powers, if he has them. This would be a big part of his development, as he'd be learning from a completely different perspective than he's used to at Camp Half - Blood.
One challenge could be dealing with the child's past traumas. If the child has been through a lot, like being orphaned or facing monster attacks on their own, Percy would have to help them heal. He's not a trained psychologist, so it would be difficult for him to know exactly how to handle it.
Poseidon is a likely candidate. Since he is Percy's father in the original series, it would make sense for him to take a more active role in raising Percy. He could teach Percy all about the ocean, its secrets, and how to use his water - related powers more effectively.
Perhaps he has been exposed to some sort of deadly and unknown substance in the mythical world. This could be a new type of monster venom or a strange plant that he accidentally ingested. The substance could be attacking his body from the inside, causing his internal organs to bleed, and thus he throws up blood.
I'm not sure specifically as there could be many different 'playing with fire' Percy Jackson fanfics. It might involve Percy getting into a dangerous situation that's like playing with fire, perhaps dealing with a powerful and unpredictable enemy or a risky magical situation.