I am citizen of Turkey and working in Northern Cyprus. I want to apply for Green Card. How should i mention my country of residence? Should it be Turkey or Cyprus?
Since the US does not recognize an independent country in northern Cyprus, where you reside, you should select Cyprus. You certainly do not reside in Turkey, since no state considers northern Cyprus to be part of Turkey.
You suggest in a comment that international mail must be addressed to Turkey, which makes sense if no other country recognizes Northern Cyprus. I would therefore choose Turkey for the country (item (g)) in the mailing address (item 8), and Cyprus for the "country where you live today" (item 9).