Some fanfictions have a plot where Percy's crush on Artemis causes trouble among the gods. Since Artemis is a virgin goddess, the other gods might see Percy's feelings as a threat to the order of the divine world. This then leads to Percy having to face various challenges to prove his intentions are pure or to simply stay away from Artemis.
There's also a fanfiction called 'Percy's Forbidden Love'. This one is a bit more angsty as Percy realizes that his crush on Artemis can never be fulfilled due to her divine nature and her vow of chastity. It explores his pain and acceptance of the situation.
This is a rather disturbing concept for a plot. But hypothetically, Percy could be in a situation where he is Artemis' slave and is made to perform tasks that are against his will. He might meet other characters who either help or hinder his attempts to gain freedom. But again, this is not a very positive or common type of fanfiction plot, and most fanfiction writers would probably avoid such a dark and unethical concept.
One interesting plot could be that they have to face a new threat together as a married couple. For example, a powerful ancient monster awakens and they combine their unique skills - Artemis' hunting and Percy's water - related powers to defeat it.
One possible plot could be Percy trying to win Artemis' acceptance. He might go on dangerous quests to prove his worth. Another plot could be Percy leaving the demigod world altogether and trying to find a new identity away from his unwanted connection to Artemis. Maybe he would join forces with some outcast creatures from Greek mythology who also don't fit in.
One possible plot could be Percy being betrayed by someone he trusted in the context of Artemis' world. Maybe a fellow demigod turns on him due to jealousy of his relationship with Artemis. Another could be Artemis herself being betrayed by a member of her hunt, and Percy gets caught in the middle trying to help her.
A plot could also center around the baby's identity and how it fits into the existing world of Percy Jackson and the Olympians. The baby might be seen as a symbol of a new era, a bridge between different pantheons perhaps. And it could face difficulties in being accepted by both the mortal and the divine worlds.
One interesting plot could be a new adventure where the Hunters of Artemis have to team up with Percy Jackson to defeat a powerful ancient monster that has awakened. This would involve a lot of action, with the hunters' skills and Percy's unique powers working together.
A great plot could involve Percy having special powers due to being Artemis' child. For example, he could have enhanced archery skills and an affinity for nature, like being able to communicate with animals in a deeper way. He might also be involved in a plot where he has to protect Artemis' sacred places from those who would desecrate them, leading to epic battles against powerful enemies.
Well, she could betray Percy by revealing his secrets to his enemies. Maybe she's forced to do so under some kind of magical compulsion or threat.
One popular plot could be Percy going on a quest to protect something that is dear to Artemis. For example, he might have to safeguard an ancient relic that is crucial for her domain. Another could be Percy having to prove his loyalty to Artemis in the face of opposition from other gods who don't trust his intentions. And sometimes, it's about Percy and Artemis teaming up to face a common enemy that threatens both of them and their worlds.