Dear Ms. DeDonato,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog for anyone in the 17th Infantry, Company G from Connecticut and found 174 file units from the series Indexes to the Carded Records of Soldiers Who Served in Volunteer Organizations During the Civil War, 1899 - 1927 in Record Group 94. We hope your great-grandfather is listed.
We also suggest that you conduct a search of the Compiled Military Service Records (CMSR) in the Catalog and the pension files for him as well via the National Archives at Washington, DC (RDT1). Please contact RDT1 using their email address. These records are also available on ancestry.com and/or familysearch.org.
We hope this information is helpful. Best of luck with your family research!