Who established his own colony because of a dispute with church leaders in New England?
Roger Williams created the colony of Rhode Island after arguing with religious leaders in New England.
Roger Williams was a baptist in the Ana Baptist movement's tradition. While the Puritans and the Baptists were both non conformists to the traditions of the Anglican Church they did not agree with each other.
The Puritans believed strongly in infant baptisms, that baptizing the infant children of believing parents ensured the child's acceptance into heaven. The Ana Baptists dating back to 200 AD had taught that infant baptist was not enough that adults had to be baptized as an expression of their personal faith and belief in Christ. ( hence the name Ana Baptist or rebaptizer Eph 2:8 It takes personal faith to be saved. )
Roger Williams was preaching the doctrines of the Baptist tradition in Puritan New England. The Religious leaders of the Puritan church did not appreciate Roger Williams theology that contradicted theirs. The Puritan leaders of the church were also the political leaders of New England. Roger Williams was given a choice to conform to the teachings of the Puritan church or leave.
Roger Williams a non conformist in England was also a non conformist in New England. Forced to leave New England in the middle of winter he traveled south to Rhode Island and established a new colony where there was less pressure to conform to the established religious and political structures that existed in New England at the time.