The rolls for the 1st NJ Regiment (Continental) are on National Archives microfilm Micropublication 246 ("Revolutionary War Rolls"), rolls 55, 56 and 57.

You can ask your local library to borrow these by inter-library loan. Many libraries subscribe to Ancestry, which has the images from these in its site, but using the microfilm is much much faster because you don't have to wait for pages to load.

All free white able-bodied males aged roughly 16 to 60 (varies by time and place) were supposed to be available for County militia duty, which would include showing up at regular drills. Sometimes there are surviving muster rolls, sometimes not. For Warren/Sussex, I think not.

There is a large ledger with non-obviously arranged militia lists (not identified as such, and with no specific date-ranges) in the NJ Archives in Trenton, but to tell what pages of lists go with what place you have to have done a lot of neighborhood research. Since the ledger is a non-contemporaneous copy there are bound to be errors and omissions.

There may be County Court items regarding militia activities, but unless there were extensive claims for reimbursement for active-duty service or for property losses, there are unlikely to be lists. Militiamen seldom saw active duty since they were supposed to serve within the County (there are some major exceptions, but I don't happen to know of any for Sussex Co.). But especially in 1778 and 1779 there would have been patrols along the Delaware River, especially the Mine Road.

Good hunting,
Jade