Are you looking for records of Confederates held prisoner by the Union who were granted parole, Union soldiers granted parole by Confederates, or Union soldiers held prisoner by the Union Army (for violations of military law) who were granted parole?
In any case, records of that type would most likely be in the custody of The National Archives in Washington, DC. See here for their contact information: https://www.archives.gov/dc
Many National Archives records related to prisoners of war have been digitized by Ancestry and combined into the following database: https://www.ancestry.com/search/collections/civilwarpow/
Ancestry can be accessed for free at any National Archives location, and also in some public and university libraries.