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Dear M P,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog for enlistment information and located 6 series of the New Jersey State Office in the Records of the Selective Service System (World War I) (Record Group 163). Two of them are in the custody of the National Archives at New York (RE-NY) (email: email@example.com) and 4 of them are in the custody of the National Archives at St. Louis (RL-SL) (emal: firstname.lastname@example.org).
Using all of these records, you may be able to compile the listing you seek.
We hope this is helpful. Best of luck with your search!