The book 'Aldermans in America" by William Alderman Parker has information on Thomas Alderman Jr.His parents were William Alderman b. ca 1640, d aug l, 1697 and Mary Case dau of John Case and Sarah Spencer, b Jan 22, 1660, d Aug 22, 1725, married 1679. The reason for the "Jr" is not clear. They were married in Windsor, Conn but made their home in Simsbury, Conn where Thomas was born Jun 9, 1683. He married Mary Seagrave in East Hampton, Long Island Apr 27, 1702. Some say that they were in Simsbury for a short time but they settled in Cohannsey, New Jersey.They are listed as having signed the covenant of the Church of Christ in Fairfield, N J.
Parker states "From his will we learn that by occupation he was a weaver and that leads us to wonder if he was a descendant of Robert Alderman of St Margarets, Ipswich, England, who was a cloth worker, and who, in his will dated 1639, mentions his son, William, to whom he left the shop stuff that he (Robert) still retained at the time of his death and to Robert he left money." "He was instrumental in establishing the Fairfield Presbyterian Church May 19, 1708--" Parker could not identify definitely the parentage of William Alderman or his place of birth. You should be able to find a copy of the book in a genealogy library. I can send you copies of the pages if you cannot. I do not know of any new information concerning William.