I’m not familiar with the "draft registrations"

Here’s information on Jasper of the 44th

Jasper Thompson, 18 year old Farmer, born in Ray County, Missouri, enlisted August 18, 1864 at Richmond, Missouri for the war, blue eyes, dark hair, fair complexion, 5’ 7”, mustered in at St. Joseph, Mo. September 9, 1864, Company F, 44th Regiment Missouri Volunteers, mustered out at Vicksburg, Miss. May 18, 1865

M405: Compiled Service Records of Volunteer Union Soldiers Who Served in Organizations From the State of Missouri.

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Died July 26, 1925 at Camden, Mo.

Served also with C 4 Prov. En Mo Mil ???

T289: Organization Index to Pension Files of Veterans Who Served Between 1861 and 1900.