My Faron ancestors settled in Millbury, Massachusetts, just south of Worcester, and many of them are buried in St. Bridget's cemetery there. (Therefore, Catholic.) Many worked in mills in southern New England up to 1950.
There are many Faron descendents from Michael & Rosa, the parents who brought their seven children to America. I've connected with a couple of contemporary cousins (sharing the same gggrandfather).
Re the spelling of the name -- US records have it all over the place; I've seen the three mention plus a half dozen more. My research into Armagh has the spelling as Fearon.
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I think, if we have a connection, it will be a couple of generations back in Ireland.