Dear Ms. Pardee,
Thank you for posting your request on History Hub!
There are two main series that provide a record of service of Regular Army enlisted soldiers for this time period. One is the Registers of Enlistments in the United States Army, 1798 - 1914 in the Records of the Adjutant General's Office, 1762 - 1917 (Record Group 94) that was microfilmed as National Archives Microfilm Publication No. M233 and is the source of the scanned records that you viewed on Ancestry. The other is the record series Enlistment Papers, 1798 - October 31, 1912 in Record Group 94, the bulk of which has not been microfilmed or digitized. There may also be a pension file for him but most have not been digitized.
To order records that have not already been digitized, please fill out a NATF Form 86 for the service records and a NATF Form 85 for the pension records and mail the completed forms to the address listed on the form. You also may place your order online using eservices.archives.gov. 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. 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 is helpful. Best of luck with your research!
Thank you, Mr Atkinson.