Mathis Brothers

My uncle remembered a statement my Grandfather made years ago. My grandfather was told that his family was Scots-Irish and that three brothers immigrated to America. He wasn't given the year of immigration or their names, but of the three brother's, one died shortly after arriving, another was hung as a horse thief and the one who survived is our families direct line. The earliest Mathis that I can confirm is a direct line to our family is Jacob Mathis AKA Jacob Mathews b. abt. 1817 in North Carolina.
Thank you.