Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. There are stories that explore Catwoman's relationship with Batman in the Arkham Knight universe in various ways, such as her adventures during the events of the game, or her backstory and how it ties into the overall Arkham Knight narrative.
Archive of Our Own (AO3) is a great place to start. It has a large collection of fanfiction, and you can easily search for Batman Arkham Knight Catwoman fanfiction there. Just use the search bar and type in relevant keywords.
In this fanfiction, it could be interesting if Catwoman discovers a secret about the Arkham Knight that Batman has overlooked. She could use this knowledge to her advantage, either to make a deal with the Arkham Knight or to help Batman. For example, she might find out that the Arkham Knight has a weakness related to a certain location in Gotham that was important to his past. Catwoman could then lead Batman there to take down the Arkham Knight.
For Batman, his character could be developed by showing more of his internal struggle. In the Arkham Knight scenario, he's facing a lot of challenges. Maybe he starts to question his no - kill rule more when he sees the destruction the Arkham Knight is causing. With Catwoman, her thieving skills could be explored in more detail. She could use her skills not just for personal gain but also to help the people of Gotham in a more subtle way.
The Catwoman story in Arkham City is mainly about her navigating the dangerous and chaotic Arkham City. She has her own set of goals, often involving stealing valuable items. She also gets involved in the larger conflicts in Arkham City, interacting with other characters like Batman. For example, she might be after a particular jewel or artifact while also having to deal with the various gangs and super - villains that populate the city.
The Catwoman story in Arkham City isn't too lengthy. It adds an exciting dimension to the game, but you can finish it within a reasonable amount of time, depending on your gameplay style and how much you explore.