From 1795 to 1918, neither Lithuania nor Poland existed as independent states. All of Lithuania and a good portion of Poland were under Russian occupation.
Kapciamiestis would have been part of the Suwalki/Suvalkija gubernia (Russian for province). The land area covered by the Suwalki/Suvalkija gubernia are in both present day Lithuania and Poland. Some records for what is now Lithuania can be found in the Suwalki regional archive.
Both of my mother's parents came from Lithuanian villages in Suwalki/Suvalkija. I believe some of pertinetn records are in the Suwalki archive but I have yet to write them.