What information do you already have indicating that he served? Might he have done so under an alternate name or spelling? The reason I ask is because I found a Ancestry Family tree page for "Harvey Matevia" which cites the U.S. Army, Register of Enlistments, 1798-1914 without linking the document or giving a precise enlistment date, however no matter what search terms I used I couldn't find anything for him when I searched the records myself.
Dear Mr. Matveia,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series Enlistment Papers, 1798 - October 31, 1912 in the Records of the Adjutant General's Office, 1762 - 1917 (Record Group 94) that may include his military service files if he served in the Regular Army. We also located the Carded Records Showing Military Service of Soldiers Who Fought in Volunteer Organizations During the Philippine Insurrection in Record Group 94 that may include his service files if he served in a volunteer unit from Michigan.
To request a copy of his service record, please download the NATF Form 86, fill it out to the best of your knowledge, and mail the completed forms to the address listed on the form. There also may be a pension record for him that may be ordered using NATF Form 85. If you believe he may have used variant spellings or alternate names, please include that information in your order. For more information see Requesting Copies of Older (pre-WWI) Military Service Records.
Please note that the National Archives and Records Administration (NARA) has suspended reproduction and digitization services until further notice due to COVID-19. Orders will not be serviced until operations can resume safely. NARA has also temporarily suspended the option for placing online orders using eservices.archives.gov. Once operations resume, document reproduction requests will be filled in the order in which they were received. We apologize for any inconvenience.
We hope this information is helpful. Best of luck with your research!