This is the 7890th most frequent Russian word.
каспийске
"Каспийске" is not a standard Russian word, but it may relate to "Каспийский," meaning "Caspian," as in the Caspian Sea.
The word 'Каспийске' in this sentence is part of the proper name 'Каспийское море,' referring to the Caspian Sea. It is in the genitive case to indicate the location at 'Каспийском море.'
Когда ты последний раз был на Каспийском море?
When was the last time you were at the Caspian Sea?
Here, 'Каспийский' modifies 'побережье' to describe the coastline related to the Caspian Sea. It is in the instrumental case for the noun 'Каспийском.'
Фауна на Каспийском побережье очень разнообразна.
The fauna on the Caspian coast is very diverse.
In this sentence, 'Каспийский' is used as an adjective to signify the region associated with the Caspian Sea. It shows a complex noun phrase 'Каспийского региона.'