I can offer no guarantee as to the accuracy of the information, but looking around online this is what I'm seeing, beginning with Enoch and proceeding to his parents, grandparents, &c:
Enoch Alderman - b 1801, Duplin Co, NC John and Nancy Ann (Newton) Alderman John and Mary (Cashwell) Alderman Daniel and Abigail (Harris) Alderman Thomas and Mary (Seagrave) Alderman
Thomas was born 11 Jan 1683, in Hartford Co, Connecticut, and subsequently removed to Cohansey Co, New Jersey. He was a son of William Alderman - the earliest known ancestor of this line, who died in 1697, Hartford Co - and Mary Case.
Other researchers of this line seem to be referencing William Alderman Parker's book, Aldermans In America, which I do not own myself, but probably has more specific information.
I descend from Thomas Alderman's youngest brother, Joseph.