This is the 8418th most frequent Russian word.
нагайбакского
"Нагайбакского" refers to something related to the Nagaybak people, a small ethnic group in Russia, or their language.
In this sentence, 'нагайбакского' is used as an adjective in the genitive case describing 'народа' (the people).
Я читаю книгу о нагайбакского народе.
I am reading a book about the Nagaybak people.
Here, 'нагайбакского' is an adjective in the genitive case modifying 'происхождения' (origin).
Эта музыка нагайбакского происхождения.
This music is of Nagaybak origin.
In this example, 'нагайбакского' serves as an adjective in the genitive case describing 'искусства' (art).