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The "patriarch" Francis, that is the English (probably not Welsh) immigrant to the Colony of Rhode Island & Providence Plantations in the late 1600s, was illiterate, so I doubt very much that he came from any kind of landed gentry in England that could lay claim to a coat of arms.
Francis and wife Anna both used their marks to sign their numerous land records in Westerly, RI, between 1693-1718. Their son Francis, born in America, was the first to sign his own name.
Note that Francis actually lived in what today is farm country just north of the village of Shannock, in the Town of Richmond -- this was still part of Westerly in Francis' time. Moreover, he was a member of the Second Sabbatarian Church of Newport, which was actually in what today is the village of Ashaway in the town of Hopkinton, RI -- Ashaway was also in Westerly in Francis' time.