Archive records of the actual serial numbers of carbines or revolvers issued to particular units or soldiers are very scarce. That's because such listings were not required to be kept by the military, and the rare lists surviving are examples of unnecessary recordkeeping that survived by accident and were discovered in the archives by accident.
Although the various units were required to make reports of the types and numbers of arms on hand, neither the Union nor Confederate military had any requirement that the serial number of a gun should be recorded as it was issued to a soldier or sailor.
Serial number lists in the archives are typically found in Cavalry Company Day Books, where some solder who was a store clerk in civilian life made the sort of inventory he had kept in civilian business.
Where I have seen actual photocopies of such lists, the serial numbers were part of a more comprehensive chart showing for each trooper the type and amount of equipment he had (and was responsible for), most of it horse tack, such as saddles, halters, curry combs, hoof picks, saddle blankets, as well as saber, revolver and carbine.
This was not a report required to be kept of these serials, but the writer added that info to a general equipment listing kept for his cavalry company, and sometimes such a list survived and is discovered.
I think of these lists as similar to the penciled grocery lists I have made over the decades. I have made hundreds of grocery lists to use same week I made them and then threw them away – there may be a few that have survived by accident (such as if I used one as a bookmark,) but my hundreds of grocery lists were not required forms, were made for my own immediate use, not required to be retained, and so pretty much all thrown away over the years.