In some fanfiction, they interact as reluctant allies. They might start off distrusting each other due to the nature of the Games but gradually come to respect one another's abilities.
Honestly, it's hard to name just a few. However, some authors who seem to really get into the nuances of Finnick and Katniss's characters are often those who are also big fans of the original series. They study the books closely and are able to write fanfiction that feels true to the source material. You can start by looking at the works of authors who have been writing Hunger Games fanfiction for a long time as they likely have some great Finnick and Katniss stories as well.
One great fanfiction could be about Finnick and Katniss teaming up in the arena in a way that wasn't shown in the original books. They use their unique skills to outwit the Capitol's new and devious traps.
One interesting fanfiction could be about Finnick and Katniss teaming up earlier in the Games and using their unique skills to outwit the Capitol's traps. For example, Finnick's charm and fishing skills combined with Katniss's archery and survival instincts make them a formidable duo.
Johanna could also be included. She has her own rough past and strong personality. Her interactions with Finnick are already established in the original story, and her relationship with Katniss could be developed further. They could all form a sort of misfit group fighting against the Capitol's tyranny.
A fanfic could explore a scenario where Finnick saves Katniss's life in a different way. Instead of in the arena, it could be in a Capitol raid. Finnick uses his knowledge of the Capitol's layout and his combat skills to keep Katniss safe. This could lead to a deeper connection between them as Katniss is indebted to Finnick for her life.
Finnick from The Hunger Games was a complex character. He first won his Hunger Games at a young age. His beauty made him a favorite in the Capitol, but it also came with a price. He had to endure the Capitol's immoral demands. In the later games, like the Quarter Quell, he showed great courage. He fought alongside Katniss against the Capitol's forces. His relationship with Annie was a bright spot in his otherwise difficult life. He was a strong fighter, using his trident skills to stay alive in the deadly arenas.
One of the main themes is often trauma and recovery. Finnick has been through so much in the original story, and fanfiction often explores how he copes with that. For example, in many stories, his experiences with the Capitol are further dissected and his path to getting over those traumas is detailed.
One great Finnick and Annie fanfiction is 'Annie's Song'. It beautifully portrays their relationship. It delves into how Finnick's past in the Games affected his love for Annie and how she was his salvation. The story is full of tender moments between them and also shows their strength as individuals in the cruel world of Panem.
One great Finnick OC fanfiction is 'Finnick's New Beginning'. It creates a really interesting original character who teams up with Finnick in the arena. The story is full of action and the relationship between Finnick and the OC is developed really well.