Betty-
I've never heard of any required oath of allegiance in New Jersey. The Oath of Allegiance in PA was for arriving immigrants who were not English citizens (primarily the PA Germans) and the oath was that of allegiance to the government of the Pennsylvania colony and to the English King--not to the Patriot cause.
It sounds to me as if you are looking for evidence as to whether your New Jersey Revolutionary War era ancestor did anything that would qualify as Patriotic Service for acceptance by DAR.
Why not post a lookup request to this board so that the volunteers can see whether your ancestor is listed in the Patriot Index? Perhaps proof has already been filed.
Joan, message board admin