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Dear Royal Magnell,
Thank you for contacting the History Hub!
The Union army kept records of Confederate soldiers captured and killed in many different places. Many of these records are from prisons. For example, the Registers of Confederate Prisoners at Camp Morton, Indiana, 1889 - 1904, lists the “name, rank and organization of the prisoner; the date and place of his capture; and remarks.” The Death Register of Confederate Prisoners at Johnson's Island, Ohio, 1889 - 1904, lists “name, rank, and regiment or residence; date and place of capture; date of arrival; date of death; disease; sometime the grave number; and remarks.” However, this data collection was not standardized and some examples of these lists have date and place of capture while some do not. The National Archives blog NARAtions has a very helpful post, “Family Tree Friday: Confederate prisoner of war records.” It goes into detail about how and where to find these types of records.
The National Archives has also microfilmed M598, Selected Records of the War Department Relating to Confederate Prisoners of War, 1861-1865. This has been digitized through FamilySearch.com and is available online here. For more detailed information about this series, you can visit their information page here.
While you say that you are looking for Union army records, the National Archives has microfilmed the Confederate States Army Casualty Lists and Narrative Reports, 1874 - 1899, which has much of the information you are looking for from the Confederate side. This can be accessed online through Fold3.com here. More information about these records can be found in this pamphlet (PDF). Other Confederate records that may be helpful include Muster Rolls of Paroled and Exchanged Confederate Prisoners of War, 1874 - 1899 and Notes Relating to Confederate Prisoners, 1889 - 1904. (Our website has a detailed contents list of the War Department Collection of Confederate Records (Record Group 109).)
When searching the National Archives catalog, it may be helpful to use the search terms “Confederate” and “date and place of capture” to find records most helpful to your search. This link will take you to those search results now.
We wish you all the best with your research.