In the comics, Asami and Korra are indeed together. Their connection deepens and they form a significant partnership. The storylines show their bond growing stronger.
One possible fanfic could be about Asami getting jealous when Korra spends a lot of time with another character. Maybe Korra has to work closely with someone on a new project in Republic City, and Asami starts to feel left out. Asami might try to hide her jealousy at first, but it eventually bubbles to the surface during a dinner with Korra and the others.
She could also get angry. Korra is a strong - willed character. After the shock wears off, she might lash out at Asami. She could yell and demand an explanation. She might feel that she has been wronged and wants Asami to know how much she has hurt her.
You can find korra and asami fanfiction on websites like Archive of Our Own (AO3). It has a large collection of fan - made stories. Fanfiction.net is also a good place to look. There are likely to be many korra and asami fanfictions there as well.
There are many korra and asami fanfictions out there. For example, 'The Festival of Unity' could be a story where they participate in a festival that celebrates the unity of different cultures in their world. It would show how they interact with others and strengthen their own bond. 'The Training Days' might be about them training together, sharing their skills and learning from each other. 'The Quest for Peace' could involve them going on a quest to bring peace to their land, relying on each other every step of the way.