Another name for Thomas was Capt. Thomas "the Immigrant" Jefferson.
Sources differ on the name of his father. It was either John Jefferson or Samuel Jefferson. In at least one source (http://www.gencircles.com/users/kristinhopper/4/pedigree/5673), Samuel is the father of Thomas, and John Jefferson, a member of the first elected assembly at Jamestown, is Samuel's father.
Thomas married Mary Branch, daughter of Christopher Branch Jr. and Sarah Almond. (Mary Branch was born in 1657 in Flouer Dieu Hundred, Wetzel, Henrico, Virginia, (United States).)
1 http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi, http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=family8jun10&id=I48673.
Website - Genealogy, http://www.gencircles.com/users/kristinhopper/4/pedigree/5673.