This is the 14425th most frequent Polish word.
przemyskie
"Przemyskie" refers to something related to Przemyśl, a city in southeastern Poland.
In this sentence, 'przemyskie' acts as an adjective that describes the landscapes associated with the region of Przemyśl.
Przemyskie krajobrazy są przepiękne.
The landscapes of Przemyśl are beautiful.
Here, 'przemyskich' is the genitive plural form of the adjective, modifying 'tradycji' (traditions), showing possession or association to the city of Przemyśl.
Zajmuję się badaniem przemyskich tradycji.
I am studying the traditions of Przemyśl.
In this case, 'przemyskich' is used to describe 'studentów' (students), indicating that they come from the region associated with Przemyśl.