Saphira is often a popular character. Since she is Eragon's dragon, she can add a lot of depth to the story. Her unique abilities and her relationship with Eragon can influence the interactions between Eragon and Murtagh in the fanfiction.
The OC could be integrated into the story by having a shared past with either Eragon or Murtagh. Maybe they grew up in the same village as Eragon but were separated when the Ra'zac attacked. Years later, they reunite and the OC can offer some unique perspective or ability to the situation. Or, if the OC has a connection to the dragons in a different way than Eragon and Murtagh. For instance, the OC might have a special bond with a dragon that was thought to be lost. This would bring them into the story as they try to protect their dragon friend and get involved in the events related to Eragon and Murtagh. Also, the OC could be a trader who has information about the movements of the enemy forces. They could trade this information to Eragon and Murtagh in exchange for protection or some other favor, thus becoming part of the story.
A common theme is adventure. Since Murtagh is often involved in action - filled storylines, the OC usually joins him in his adventures. Another theme is romance. Writers might pair the OC with Murtagh in a romantic relationship, exploring their chemistry and how they grow together.
One great 'Harry Potter and Murtagh' fanfiction is 'The Unlikely Alliance'. It explores a scenario where Harry and Murtagh meet and have to work together against a common dark force. Their different magical backgrounds lead to some really interesting interactions.
There are some out there. Some of them explore the complex relationship between Eragon and Murtagh in a romantic way. They might delve into how their shared experiences could lead to a deeper emotional connection. However, the quality can vary, so it's best to read the reviews or summaries first.
Power dynamics also play a role. Nasuada is a powerful leader and Murtagh has his own set of powers. Fanfictions may explore how their different positions of power affect their relationship, whether it creates tension or a sense of mutual respect.
One interesting eragon murtagh fanfiction could be about their adventures together in a new land. Maybe they discover a hidden magic that was unknown in the original books.
There could be a fanfiction where Murtagh and Eragon form an unexpected alliance later in life. They put aside their past differences and join forces to fight a new, greater evil that threatens Alagaësia. This would involve a lot of character development for both of them as they learn to trust each other again.
I'm not sure which specific 'murtagh novel' you are referring to. But if it's a fantasy novel, you might like 'Eragon' by Christopher Paolini. It has similar elements of adventure and a richly imagined world.