Another option is to check out Reddit. There are Detroit: Become Human subreddits where fans often share their own fanfictions or recommend ones they've read. You can post a request specifically asking for OC x Kara fanfictions, and the community might be able to point you in the right direction.
Fanfiction.net is also a great place to look. It has a large collection of fanfictions for various fandoms, including Detroit: Become Human. However, the quality can vary, so you might need to skim through a few to find ones that really focus on the OC x Kara relationship in a way that you like.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of Detroit: Become Human fanfictions. Just use the search function and type in 'Connor x OC' to get relevant results.
Another idea is Kara getting separated from Alice and Connor during their journey to freedom. She then has to rely on her own wits and the kindness of some humans she meets along the way. This could lead to her having to make difficult decisions, like whether to trust a human who seems friendly but might be leading her into a trap. It would be a great exploration of her character's growth and her ability to adapt in tough situations.
Well, there are quite a few. You can check out fanfiction platforms like Archive of Our Own. There you might find some interesting Kara - related lemon fanfics. Some might focus on Kara's journey in the game world with unique plot twists and character developments that are quite engaging.