Zavadka is a village next to the town Humenne in Slovakia in which I live in. It is definitely not Carpathian Ruthenia. It is still area in the eastern Slovakia. Carpathian Ruthenia is the part in Ukraine next to the slovak border. Your ancestor could think of themselves that they are minor ethnicity which lives in the Slovakia corner northern and eastern from the Zavadka. This ethnicity recognise themselves as Rusini (Rutheni).