Yes, there are quite a few. You can start by looking on popular fanfic websites like Archive of Our Own. Some fanfics might focus on their relationship within the context of the family dynamics in Westeros. For example, there could be ones that explore how Catelyn's actions towards Brandon affected the Stark family in the long run.
Well, Brandon was a very different character from Catelyn. He was known for his boldness and impulsiveness. Catelyn, on the other hand, was more about duty and family loyalty. In fanfics, this contrast can be exploited in many ways. For example, a fanfic could be set in a scenario where they have to work together against a common enemy. Their different outlooks would lead to both tension and cooperation, which is really engaging to read. Additionally, their positions in the noble families of Westeros mean that any story involving them has the potential to be full of political drama and intrigue.
In the fanfic, it could be that the tourney is a cover for something more sinister. Brandon Stark senses this and starts to investigate. Catelyn, who is a friend of his family, offers to help him. As they dig deeper, they find out that their own families are somehow involved in the dark secrets behind the tourney. This revelation shakes their relationship and they have to decide whether to side with their families or with each other.
In a fanfic set during a tourney, their relationship could be explored through the traditions and events of the tourney. Brandon could give Catelyn his favor to wear during the jousting, which is a very symbolic gesture. Catelyn, in turn, could cheer for Brandon louder than anyone else. As the tourney goes on, they might face challenges together, like dealing with a drunk and rowdy knight who tries to cause trouble. Through these shared experiences, their relationship deepens and evolves.
Well, it could have led to a completely different power dynamic in Westeros. Maybe Ned would have made different alliances or faced more challenges alone.
I really liked the fanfic 'Jon Snow and Catelyn's Unlikely Bond'. In this one, they are forced to work together to save Winterfell. The story is full of action and also some really emotional moments. It does a great job of exploring their characters and how they might interact when put in a difficult situation.
Well, one type of 'Catelyn Stark bashing fanfic' might be those that focus on her actions during the War of the Five Kings. Some might depict her as being too hasty in her judgments, like when she captured Tyrion. Another could be related to her treatment of Jon Snow. However, it's important to note that bashing a character in fanfic can be a bit controversial as it often goes against the more complex portrayal in the original work.
One of the best Catelyn Stark stories is her role in the Red Wedding. She was so strong and full of love for her family. She tried her best to protect them, but the betrayal at the Red Wedding was heart - wrenching. Her reactions and the way she faced that horror showed her true character.
Another one could be 'When Catelyn Stark Met Harry Potter'. This fanfic could explore the relationship between Catelyn Stark and Harry Potter. Maybe Catelyn Stark becomes a mentor - like figure to Harry, using her wisdom from her own experiences in Westeros to guide Harry in his fight against Voldemort.