Hello, I am a UK citizen currently living in Cyprus. I want to apply to go to China

I do not hold a Cypriot passport (Did not feel the need to as a UK passport holder), however i am entitled to live here as my father was born in Cyprus. This means i do not need to have a work permit or residence permit.

I want to travel to China for an exhibition next month and was wondering if it was possible to apply through the Chinese embassy in Cyprus. If yes, then what would be the required documents, and would any problem occur because of no work/residency permit?