May have lived on Isle of Lewis, as it was reported by a 6th generation daughter, they perhaps owned the island. James' father may be James Mathewson who's siblings are John, Joseph, Gilbert, Hugh Thomas, James (in order of birth).
John Mathewson was born before 1687.
Joseph was b. in Ayreshire and 30 years after arriving in Ireland went to Co Waterford (per 112 circa 1912) or Westneath (per 112 circa 1912).
Gilbert - no info
Hugh Thomas was born in Ayreshire, emigrated to Co Tyrone then 30 years later to Co Waterford. (as per 112 cir 1912/13) or Westneath and his name was Hugh (per 112 cir 1912/13).
James - may have been James' father.
John (of Montreal) Mathewson, son of James Mathewson (Mathewson-278) was the only relative to speak on the subject of Ayreshire be place of origin.