The Twersky Skver Hasidic dynasty line emanating from Skvyra eventually settled in the United States where part of the community founded their own township called New Square (Skvyra being pronounced as "Skver" in Yiddish) in Rockland County, New York.
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It is the administrative centre of the Skvyra Raion (district), and is currently a municipality of raion subordinance.