The index to naturalization petitions 1914-1982 for the US District Court for New Jersey (Newark Term) is located in the National Archives branch in New York City.
The records are also at the same location and can be ordered on-line https://catalog.archives.gov/id/604960
Dear Ms. Glock,
Thank you for posting your request on History Hub!
In addition to the information from the previous poster, we suggest that you request an index search through the US Citizenship and Immigraiton Services (USCIS) Genealogy Program to identify any naturalization records for your father. You may order any records through the same site.
The US Citizenship and Immigration Services (USCIS) maintains duplicate copies of court records (including the certificate of citizenship) created September 27, 1906-March 31, 1956 within Certificate Files (C-Files). Beginning April 1, 1956, INS began filing all naturalization records in a subject’s Alien File (A-File). Please consult NARA’s web page on Alien Files (A-Files) for more information.
We hope this is helpful. Best of luck with your family research!
Your father will likely have a sizable file with USCIS Genealogy Program, as noted by Cara Jensen. If he naturalized before 1 April 1956, he will have a C-File. If he naturalized on/after 1 April 1956, he will have an A-File.
An A-File for him does not immediately appear in the NARA catalog, so it is likely still with the USCIS Genealogy Program.
You might first try obtaining his naturalization records from Somerset County Courthouse - Clerk's Office. This may help you more easily order his record from USCIS Genealogy Program.