I really like the fanfic 'Percy and the Prince's Arrangement'. It takes the concept of an arranged marriage and flips it on its head. Percy is hesitant at first, but as the story progresses, he realizes that there's more to the prince than he thought. The author does a great job of building the relationship slowly, with lots of moments of doubt and discovery.
Love against all odds is a big theme. In these fanfictions, Percy and the prince often start off not liking each other or at least being very skeptical. But as they get to know each other, they find love in this situation that was forced upon them. Also, the theme of self - discovery is present. Percy discovers new sides of himself as he navigates this new relationship and the royal life.
One common trope is the 'Reluctant Partners'. Percy or the other character involved is usually very reluctant about the arranged marriage at first. They might resist it and try to find a way out. For example, Percy might think it goes against his free - will and his loyalty to his friends and previous relationships.
One really interesting Percy Jackson arranged marriage fanfiction is 'The Forced Bond'. It explores how Percy and Annabeth are forced into an arranged marriage by the gods for some political reasons. It's full of their usual banter but with the added tension of the arranged situation.
Another theme is the growth of their relationship. They usually start off as strangers or even enemies in some cases, but as they are made to be together, they gradually learn to understand and care for each other. This can involve dealing with family drama, as their families might have different expectations from the marriage. For example, in some fanfictions, their families are trying to gain power through this union. And also, they might face external threats or challenges that bring them closer together.
The Titans could also serve as antagonists. If they sense that the union of Percy and Artemis could strengthen the power of the gods, they would do everything they can to stop the marriage. They could send their minions to attack Percy and Artemis, or they could try to corrupt one of them, perhaps by offering Percy great power in exchange for abandoning Artemis, or by making Artemis believe that Percy will bring destruction to her followers if she marries him.
One possible plot twist could be that Percy and Thalia initially resist the arranged marriage. Percy might be in love with someone else, like Annabeth. But as they are forced to spend time together for the sake of the arranged union, they start to discover each other's hidden qualities. Thalia could reveal her vulnerable side to Percy, and Percy could show his loyalty and courage in a new light to Thalia. This could gradually lead to them developing real feelings for each other, despite their initial reluctance.
A plot could revolve around the cultural clash between Percy, a demigod used to a more modern and sometimes chaotic world, and Artemis, a goddess with her own very strict and ancient ways. The arranged marriage forces them to navigate this. Maybe Percy tries to introduce Artemis to things like modern music or movies, which she initially scoffs at but later starts to enjoy. In the process of trying to make the best of the situation, they could also face challenges from other mythological creatures who see their union as a threat to the existing order of the mythological world.
There's also 'A Marriage of Convenience' which is really interesting. In this story, the arranged marriage between Harry and Percy is more of a strategic move to unite two powerful wizarding families. As they start living together, they discover new sides of each other and their relationship evolves in unexpected ways. They have to deal with jealous rivals and family expectations, which makes for a great read.
Percy is very much in touch with his emotions, which can be both a strength and a weakness. Thalia, on the other hand, often tries to hide her emotions behind her tough exterior. In an arranged marriage situation, this could lead to clashes. Percy might try to get Thalia to open up too quickly, which she would resist. But over time, Percy's emotional openness could help Thalia come to terms with her own feelings. And Thalia's ability to keep her cool in tough situations could help Percy learn to be more composed when he's feeling overly emotional.