Here are the post war Amnesty Oath records, I am not aware of war time parole/oath records.
These are found at Fold3.com
"Amnesty Papers," 1865-1867
Case Files of Applications from Former Confederates for Presidential Pardons ("Amnesty Papers"), 1865-1867, M1003
At the end of the Civil War, President Andrew Johnson’s proclamation of May 29, 1865 provided for a general amnesty with some exceptions. Former Confederates not covered by the general amnesty were required to request a pardon and amnesty. These requests were evaluated on a case-by-case basis. This series of images contains the individual letters of application and other records in response to the proclamations, and a few applications submitted to President Lincoln while he was president.
The applications consist of statements of the petitioner and an oath of allegiance. In many files there are recommendations from prominent citizens for clemency, or letters from relatives or friends asking for compassion.
Approximately half of the applications are from individuals excepted under the proclamation of May 29, 1865 because of their ownership of property valued at more than $20,000. Under Johnson’s proclamation there were 14 classes of persons were not covered under the General Amnesty (the first seven were from previous amnesty proclamations during the Lincoln administration):
diplomatic agents or officials of the Confederacy,
persons who left judicial posts under the United States to aid the rebellion,
Confederate military officers above the rank of Army colonel or Navy lieutenant,
members of the U.S. Congress who left to aid in the rebellion,
persons who resigned commissions in the U.S. Army or Navy and afterwards aided in the rebellion,
persons who treated unlawfully black prisoners of war or their white officers,
persons in military or civilian confinement or custody,
individuals who had absented themselves from the United States in order to aid the rebellion,
graduates of West Point or Annapolis who served as Confederate officers,
ex-Confederate governors,
persons who left homes in territory under U.S. jurisdiction for purposes of aiding the rebellion,
persons who engaged in destruction of commerce on the high seas or in raids from Canada,
voluntary participants in the rebellion who had property valued at more than $20,000, and
persons who had broken the oath taken under the provisions of December 8, 1863.
President Johnson would issue three later amnesty proclamations. One, which reduced the number of excepted classes to three, reducing the number of cases to about 300. His second proclamation covered all but a few Confederates, including Jefferson Davis and Robert E Lee. On Christmas Day 1868, Johnson’s third proclamation gave amnesty to all unconditionally, and without reservation to all who had participated in the rebellion.
These records are also called “Case Files of Applications from Former Confederates for Presidential Pardons” or “Pardon Petitions and Related Papers Submitted in Response to President Andrew Johnson's Amnesty Proclamations of May 29, 1865, (“Amnesty Papers”)”.