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 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.
Percy could lose trust in the gods completely. After Artemis' betrayal, he might feel that he can't rely on any of them anymore.
In these fanfictions, a common theme is often the struggle against fate. Artemis being in the role of a slave goes against her nature, so she may fight against this imposed status. Also, themes of loyalty can come up. Characters might be torn between their loyalty to Artemis in her new situation and their loyalty to the existing order in the Percy Jackson world.
Well, in such a disturbing scenario, she could face social ostracism within the fanfiction's universe. Other characters might shun her for her heinous act.
One possible plotline could be Percy going through some sort of extraordinary adventure that changes Artemis's view of him. Maybe he saves her in a way that no one else could, and this new - found respect and connection gradually turns into love, leading to their marriage.
Another motive could be a difference in ideology. If Percy believes in a different way of handling things compared to Artemis, and he feels that her methods are endangering the world or his loved ones, he might decide to betray her in order to stop her from following her current path.
One possible plotline could be that Percy has been wronged by Artemis in some way, perhaps she made a decision that put Percy or his friends in danger, and now he's out to punish her by thwarting her plans. For example, if Artemis made a deal with a villain that backfired on Percy's team, Percy might seek revenge.
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.
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.