This is the 8624th most frequent Polish word.
pszczyńskiej
"Pszczyńskiej" refers to something related to Pszczyna, a town in Poland.
The word 'pszczyńskiej' is used here as an adjective derived from the proper noun 'Pszczyna', describing the school as located in or associated with Pszczyna.
Odwiedziłem piękną bibliotekę w Pszczyńskiej szkole.
I visited a beautiful library in the Pszczyna school.
In this sentence, 'pszczyńskiej' describes the princely family as belonging to or associated with Pszczyna.
Historyk opowiadał o wydarzeniach z czasów Pszczyńskiej rodziny książęcej.
The historian talked about events from the times of the Pszczyna princely family.
Here, 'pszczyńską' is an adjective referring to the tradition as originating from or connected to Pszczyna.