Versity is often a misspelling of varsity.
Versity has no English definition.
As a noun varsity is
university.
versity
Not English
Versity has no English definition. It may be misspelled.
varsity
English
Noun
university
Derived terms
*junior varsity
*varsity letter
Usage notes
*Used attributively in the UK to describe a sports team representing a university or college, or a match involving such a team.
*Used attributively in the U.S. and Canada to describe a sports team made up of older high school or college students (generally the 3rd and 4th years of a 4-year program), as contrasted with the junior varsity team made up of 1st- and 2nd-year students.