In fanfiction, Erik's possessiveness of Charles might be an exaggeration of his character trait. He may have a sense of ownership over Charles due to their shared experiences, like founding the X - Men together. His possessive nature could also be a way to show his intense love or loyalty towards Charles, in a rather extreme way. He might think that Charles belongs with him more than with anyone else, whether it's in their mutant - related activities or in their personal relationship.
A fanfiction might start with Charles being seriously injured in an unexpected attack. Erik, who has always had a strong connection with Charles, is enraged at first. But then he realizes that he needs to be calm to help Charles. He takes Charles to a safe place and tries to find a way to heal him. Along the way, they face many challenges, both external threats and internal emotional struggles. As time passes, their bond becomes even stronger through this difficult experience.
Another place could be Fanfiction.net. However, the search functionality might be a bit less precise compared to AO3. But it still has a large collection of fanfictions. You may need to dig a bit deeper and use more specific keywords in your search, like 'Erik x Charles slash' which is sometimes used to denote YAOI content.
Often, you'll find themes like redemption in Charles and Erik fanfic. Maybe Erik has to find his way back from a dark path, and Charles is there to guide him. Also, the theme of loyalty comes up a lot. Despite their differences, they have a deep loyalty to each other in many of these stories. And there's the theme of sacrifice too. They might be willing to sacrifice their own beliefs or even their safety for the other.
Redemption is also a theme. Sometimes Erik has done things that he regrets, and Charles is there to help him find a way back. Or vice versa, where Charles makes mistakes and Erik is the one to offer support. This theme of forgiveness and growth is quite prevalent in many Charles x Erik fanfictions.
One great 'charles xavier and erik lehnsherr fanfic' is 'Mutual Understanding'. It delves deep into their complex relationship, showing how they navigate their differences. The characterizations are really well - done, staying true to their original personalities from the X - Men universe.
Often, there are themes related to their powers and how they interact with each other because of that. For example, how Erik's magnetic powers and Charles' telepathy play into their relationship. There are also themes about redemption, like Erik trying to make up for his past actions while being supported by Charles. And sometimes, the theme of them teaming up against a common enemy in a way that deepens their bond.
The fan community around them is also a big factor. Fans love to share their interpretations and ideas through fanfiction. YAOI fanfiction about Erik and Charles allows for a different perspective on their relationship, and fans enjoy reading and writing about it because it gives them a chance to delve deeper into the characters and their connection, adding new layers to their relationship that might not be as obvious in the main story.
You can try fanfiction websites like Archive of Our Own (AO3). It has a vast collection of fanfictions on various topics, including ones about Charles and Erik. Just use the search function there to look for relevant stories.
One popular theme is the struggle between their different ideologies while still maintaining their love. For example, their views on mutants and how to coexist with humans can create a lot of tension and drama in the stories.