In a 'Percy Jackson adopted by Artemis' fanfiction, perhaps Percy is exiled from Camp Half - Blood due to false accusations. Artemis, who has always been intrigued by Percy's courage, takes him in. With Artemis as his new guardian, Percy gets involved in the Hunters' battles against ancient monsters that threaten the world. He also has to deal with the jealousy of some of the other Hunters who are not happy about a male being in their midst.
One possible plot could be Percy struggling to fit into Artemis's group of hunters. Since he's male and the hunters are usually female, there would be a lot of conflict and misunderstanding at first. He might have to prove himself worthy of being part of the group, not just because he's Artemis's adopted son. He could go on a quest to retrieve a sacred item for Artemis to show his loyalty.
One possible plot could be Percy having to defend Artemis from a new and powerful enemy. Maybe a primordial being has awakened and is targeting Artemis. Percy, with his skills and the help of his friends, must fight this enemy. He could also have to deal with the politics among the gods as he tries to protect Artemis, since some gods might not be so happy about his interference.
In this fanfiction, it could be that Artemis is in a situation where she is about to be killed or lose her powers forever. Percy, being the selfless hero he is, takes on a deadly task to prevent that from happening. Maybe it involves facing an ancient and malevolent god who has a vendetta against Artemis, and Percy uses his unique abilities and the element of surprise to try and stop this god, but at the cost of his own life.
Well, it could involve Percy being tasked with protecting Artemis in a way that goes against his normal alliances. Maybe some dark force is after Artemis and Percy has to use his skills in a new and unexpected way.
One possible plot could be that the son of Artemis discovers a threat to the demigod world that is related to his mother's domain. He then seeks out Percy for help because of Percy's reputation. Together, they embark on a journey to find a magical artifact that can stop the threat.
A plot could be that Percy is given a prophecy that involves him having to form a new kind of family unit. He decides that adopting Thalia is part of fulfilling that prophecy. But in order to fully embrace this new family, they need to go on a journey to different mythological realms. In each realm, they face different challenges that test their relationship. For example, in the Underworld, they have to deal with Hades who is not too happy about their new arrangement. This forces them to rely on each other and grow closer as they overcome these obstacles.
Well, one possible plot could be Percy discovering new powers. Since Hecate is the goddess of magic, Percy might learn magical abilities he never knew he had. Maybe he starts to see magic in everyday things in a way he didn't before. For example, he could make inanimate objects come to life or use spells to protect himself and his friends. Another aspect could be his relationship with Hecate. She might be a strict but loving mother figure, teaching him about the deeper mysteries of the demigod world and how magic fits into it all.
Well, one possibility could be that Percy, already a hero in his own right, finds himself in a situation where Apollo decides to adopt him. Maybe Percy has lost his connection to Poseidon for some reason, and Apollo sees his potential. Apollo could then train Percy in new ways of using his powers, not just related to water but also in areas like prophecy or archery, which are Apollo's domains.
One possible plot could be Percy's struggle with his new identity. Since Hera is the goddess of marriage and family, Percy might find himself in a very different family dynamic. He could be thrust into the middle of godly politics more than ever as Hera's adopted son. For example, he might have to deal with the jealousy of other gods' children who see him as having an unfair advantage.
The Titans could still be antagonists. Even though Percy is now associated with Artemis, the Titans might see him as a threat or a tool to use against the gods. Kronos, for example, could try to turn Percy to his side by offering him power or by threatening those he cares about in Artemis's group.