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.
I'm not sure there are a lot of 'Percy Punish Artemis' fanfictions specifically. However, you can start by looking on major fanfiction platforms like Archive of Our Own or Fanfiction.net. Use their search functions and type in 'Percy Punish Artemis' to see if any relevant stories pop up.
Percy could try to influence the fanfiction community to ignore or avoid the Artemis - related stories. He might use his own popularity or influence within the community to persuade others that these fanfictions are not worthy of attention. For instance, he could organize discussions or debates about the negative aspects of such fanfictions.
Percy could also react with a sense of determination. Instead of being defeated by the injury, he sees it as a challenge. He starts to figure out what made Artemis hurt him in the first place. If it was a misunderstanding, he tries to clear it up. If it was something more malicious, he starts to plot his revenge. He uses his own wits and the powers he has to either heal himself or find a way to make Artemis see the error of her ways. He might also seek the help of his friends, like Annabeth or Grover, to come up with a plan to deal with the situation.
The Hunters of Artemis are very likely to show up. They are Artemis's loyal followers and would surely be involved in the search for their mistress. Annabeth could also be there. She's Percy's friend and has great wisdom, which could be useful in devising a plan to save Artemis. Grover might be another character. His ability to sense things could help in tracking Artemis or finding clues about her whereabouts.
Maybe Artemis is on a hunt when she stumbles upon Percy. She might be initially cautious, as she's a goddess and Percy is a demigod. She could question him about his presence in Texas.
Well, Artemis is a complex character herself. Perhaps she sees something of herself in Percy, like his determination or his sense of loyalty. Fanfiction often takes these qualities and twists them in new and interesting ways. She might be drawn to how Percy is portrayed in different fan - written stories, whether it's his heroic deeds or his more vulnerable moments. Reading Percy fanfiction could be a form of escapism for her, a way to explore a different kind of heroism outside of her own experiences.
One reason could be the popularity of Percy as a character. Fans might be more inclined to write about him in a dominant role because they like him better. So, they create fanfictions where he dominates Artemis.