Added cosmos tag as you're more likely to find experts in that area.
Xamarin is a general purpose platform and doesn't directly implement support for services such as Cosmos. Instead Xamarin provides a .Net Standard 2.0 base upon which you can run existing .Net Standard libraries. You can use any Cosmos or Gremlin library which supports .Net Standard 2.0 the same way you can use those libraries in any other .Net target.
From a quick search of the docs, it looks like there are several Cosmos and Gremlin packages on Nuget.org that support .Net Standard 2.0, but I'm not familiar with that domain and can't recommend specific ones for your situation.