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.
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 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 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.
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 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.
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.
Well, in some fanfictions, there could be a plot where Percy, as the son of Chaos and with his link to Artemis, discovers a hidden prophecy. This prophecy might state that only he can unite the forces of chaos and the order of Artemis's hunters to save the world from a new threat that neither side could face alone. So he embarks on a journey to convince both groups to work together, facing a lot of resistance along the way.
There's a fanfiction titled 'My Percy Crush'. In it, the mortal's crush is presented in a very relatable way. The mortal is just an ordinary person going about their life when Percy enters it. The fanfiction focuses on how the mortal tries to fit into Percy's world while dealing with their strong feelings. Also, 'The Mortal and Percy' is a good one. It shows how the mortal's feelings develop as they learn more about Percy's heroic deeds and his complex personality.
One common plotline is Percy trying to find the perfect gift for Annabeth. It could be something related to her love for architecture or Greek mythology.