This is the 8355th most frequent Russian word.
могилевском
"Могилевском" is the prepositional case form of "Могилёвский," meaning "Mogilev" (relating to the city of Mogilev) in a locational context.
Here, 'могилёвском' is an adjective derived from 'Могилёв', indicating that the university is located in the city of Mogilev.
В могилёвском университете учатся студенты из разных стран.
In the Mogilev university, students from different countries study.
In this context, 'могилёвском' describes the museum as being situated in Mogilev, modifying 'музее'.
Мы посетили экспозицию в могилёвском музее.
We visited the exhibition in the Mogilev museum.
Here, 'могилёвском' refers to a festival associated with or held in Mogilev, qualifying 'фестивале'.