After 1906 all naturalizations took place through federal courts, although some local courts were authorized to collect the paperwork. Normally one had to have resided at least 5 years in the US prior to submitting their petition for naturalization. There is the possibility that he may have started the process while serving in the US military.
naturalization in federal courts in NJ https://www.archives.gov/nyc/finding-aids/naturalization-holdings
Dear Ms. Shea,
Thank you for posting your request on History Hub!
As the previous poster mentioned, beginning on September 27, 1906, the responsibility for naturalization proceedings was transferred to the Federal courts. For access to the naturalization records of Federal courts in New Jersey, including naturalization indexes, declarations of intention (with any accompanying certificates of arrival), and petitions for naturalization, please contact the National Archives at New York (RE-NY) via email at email@example.com. In your request for a search for your grandfather’s naturalization records, please include his name (including known variants); date of birth; approximate date of entry to the US; approximate date of naturalization; where the individual was residing at the time of naturalization (city/county/state); and country of origin.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RE-NY. We apologize for this inconvenience and appreciate your understanding and patience.
In most cases, the National Archives will not have a copy of the certificate of citizenship. Two copies of the certificate were created – one given to the petitioner as proof of citizenship, and one forwarded to the Immigration and Naturalization Service (INS).
Certificates of citizenship were issued by the Federal courts until October 1991 when INS took over responsibility for naturalization proceedings. All INS records are now overseen by the US Citizenship and Immigration Services (USCIS). USCIS maintains duplicate copies of court records (including the certificate of citizenship) created since September 27, 1906 and may be requested through the USCIS Genealogy Program.
We hope this is helpful. Best of luck with your family research!