In the biography of Burell Banister who was born July 19 1779 in Prince William County, Virginia it says he was the son of John Banister born 1749 in Godshill, Isle of Wright, Hampshire England. He died 1815 back in England. Mother was Elizabeth Willis born 1754 in same place. I researched the John Banister (that is the spelling that I found not with 2 nns. if you go to Wikitree.org/index.php?title=Burrel_Bannister you can find this article.
John Bannister parents where William and Elizabeth Tutten Bannister, William born 1707 in Isle of Wright, Hampshire, England and Elizabeth Tutten born 1707 same. Maried Sept 16, 1736 in Brading, Isle of Wright, Hampshire.
These are the only documents that I have come across, There are so many Bannister, Banisters its hard to keep them straight but Carolyn
I then went to Carolyn Adel Walker's family tree and it shows John Bannister with 2 ns born to William Bannister
I also found a early virginia immigrants list on WWW.genealogy.com/cgi-bin/ifa_image.cgi?IN-000245&PN=20&...
or try Genealogy.com genealogical records. Virginia Colonial Records. 1600-1700
Alot of Banister's and alot of Bannisters. Which were some from "Isle of Wright England."
Like I said there are lots of Johns and Lots of Williams so it is really hard to put the right one with the right one.
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nice communicating with you cousin!