The only other John Roberts in the national Archives who served in the Vermont Militia, aka Green Mountain Boys is the John Roberts at the DAR # A122830 who married Edna EDNA HILLIARD. She drew his pension under W.24796.
He served under Colonel Ebenezer Allen Vermont Regiment for one year, and then 3 years under Captain Gidieon Brownson's Company, Colonel Seth Warner's Continental Regiment..
Both the Commander's were Green Mountain Boy's; ie Allen & Warner.
That's the Proper Son of John Roberts SR. Who BTW would have been 16 at the time of Ticonderoga vs. 8 years old.
The DAR record mentions no service description other then Drummer. However this John Roberts, JR. was at Ticonderoga, Hubbardton, Bennington & Saratoga
You find the Correct John Roberts who Married EDNA HILLIARD and I'll paste in his war service record from the national Archives. BUT, he was not the John Jr. from New Jersey.
Tom