Missouri Confederate records tend to be scant, misreported or nonexistent. To add to Bruce’s information:

According to NARA microfilm roll #322, Roll 12 (Compiled Service Records of the CSA 1st NE Mo Cav, G-K – Porter’s Regiment)

William Hamilton was enlisted in Company I (Capt Rufus Brown’s Company) on August 1, 1862 in Lewis County, MO for the War by Col McCullough
[This probably means he was really in the 2nd NE MO Cav, as that was McCullough’s regiment, but the regiments traveled together in NE Missouri and the government sometimes just bunched the soldiers together under Porter.]

William P. Hamilton joined Company H (Capt Leeper’s Company) on July 25, 1862 in Schuyler County, MO for 1 year. He surrendered at Lagrange, Lewis County, MO on September 22, 1862. He was sentenced to hard labor in a military prison and sent to Gratiot on March 11, 1863. He was transferred to Alton around May 7, 1863. He appears to have been released from prison on April 15 or 16, 1864 by Special Order #94 (or #97, it’s hard to read), Dept of MO– and also by posting a $2000 bond. It states he resided in Lewis County, MO.

So not much information in their records. I do not have the microfilms for the CSA 6th MO Cav.
Craig