Dear Mr. Hill,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located a series titled Indexes to the Carded Records of Soldiers Who Served in Volunteer Organizations During the Civil War, 1899 - 1927 in the Records of the Adjutant General’s Office (Record Group 94) that includes an index card for Andrew Hill - 1st Cavalry, Company E of New Jersey (File #298823971 on Roll 11 of M550).
We also located the series Carded Records Showing Military Service of Soldiers Who Fought in Volunteer Organizations During the American Civil War in Record Group 94. Most of the service records in this series have been made available via microfilm and through digitization of the microfilm. Unfortunately, the records for New Jersey have not been microfilmed or digitized. For access to and/or copies of his military service records, please contact the National Archives at Washington, DC (RDT1) via email at firstname.lastname@example.org.
We hope this is helpful! Best of luck with your family research!