This is the 13343rd most frequent German word.
bayerischem
"Bayerischem" means "Bavarian" in English, relating to Bavaria.
The word 'bayerischem' is used as an adjective in the dative singular form referring to 'Brauchtum.'
Ich habe ein Buch über bayerischem Brauchtum gelesen.
I read a book about Bavarian traditions.
Here, 'bayerischem' is an adjective describing 'Dialekt' in the dative singular form due to the preposition 'mit.'
Wir begegneten einem Mann mit bayerischem Dialekt.
We encountered a man with a Bavarian accent.
In this sentence, 'bayerischem' describes the noun 'Dorf,' also in the dative singular resulting from the preposition 'in.'