Apsheronsk is a town and the administrative center of Apsheronsky District of Krasnodar Krai, Russia, located on the Pshekha River. Population…Apsheronsk is a town and the administrative center of Apsheronsky District of Krasnodar Krai, Russia, located on the Pshekha River. Population: 39,488, [40,225 ; 39,608 ; 34,505 ; 33,400. It was previously known as Apsheronskaya.