John, The below is a section about the Abernathy or Abernethy Family compiled by The Media Research Burearu Washington D.C. that my beloved late Aunt had sent me some years ago.
Probably the first Abernathy or Abernethy in America was William, who came from Scotland to Branford, Conn., about the year 1670 and later removed to Wallingford, in the same colony, where he was married in 1673 to Sarah Doolittle. They were the parents of William and Samuel and possibly of others. It is also possible that he had further issue by his second wife Elizabeth but no children named.
The transcribtion I have also talks about earlier and Later Abernathy and/or Abernethy
Deena Abernathy Warner 3rd Great-Grand-daughter of Hugh Abernathy 1738-1826