One great fanfic is 'The Adventures Beyond Borders'. It combines the worlds of Magnus Chase and Percy Jackson in a really cool way. The characters interact in a believable manner, and the plot is full of action and adventure. It has some really exciting fight scenes and also delves into the relationships between the different characters from both series.
Another common theme is character relationships. This could be romantic relationships, like a pairing between a Magnus Chase character and a Percy Jackson character. Or it could be friendships, exploring how characters from the two different series would be friends.
Another pairing that might be popular is Jack (Magnus' sword) and Riptide (Percy's sword). It's a more unique and humorous pairing as fans might write about the two sentient weapons having conversations or competing with each other in some way.
One interesting crossover could be the characters from both series teaming up to fight a common enemy. For example, Magnus and Percy joining forces against a powerful ancient monster that threatens both the Norse and Greek worlds. This would be exciting as they both have different powers and abilities that could complement each other.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are tons of great Magnus Chase and Percy Jackson fanfics there. Just use the search function and type in the relevant tags.
Loki could be a great villain. He's known for his trickery in Norse mythology. He could manipulate events to set Magnus and Percy against each other. Maybe he wants to cause chaos between the Norse and Greek worlds for his own amusement or to gain more power.
One idea could be a quest where Magnus and Percy have to team up. Maybe there's a new threat that combines the Norse and Greek mythologies, like a monster that has the powers of both a Greek hydra and a Norse dragon. They would have to use their different skills and knowledge to defeat it.
A great beginner - friendly fanfiction is 'The Demigod Duo'. It focuses on their basic characteristics and how they work together as a team. It doesn't have too many complex plotlines. Also, 'Annabeth's Training Days' shows Annabeth's early days of training, and Percy is also involved in a fun way. It's a good start for those new to the fanfiction world of Percy and Annabeth.
I really like 'Annabeth's Secret Mission'. In this fanfic, Annabeth has to go on a solo mission and Percy is left behind worried. It delves deep into Annabeth's character, showing her strength and intelligence. The story is full of twists and turns that keep you hooked from start to finish.
There might be some fanfiction out there with such a plot, but it goes against the essence of their relationship in the original series. In the official Percy Jackson books, their relationship is based on trust and mutual respect.