The person responsible for this family tree didn't know much about military records, linking Joseph P. Staton to different Confederate soldiers. The best match is given under the name J. O. P. Staton, who enlisted at Hopkinsville KY, Oct. 19, 1861, Co. "I", 8th Kentucky Regiment. The roll for August 1, 1862, last on file, shows that Staton went home without permission. Records showing whether or not he ever returned are not available. William Staton's name appears on a roll for Co. "H", same regiment, enlisting at Hopkinsville KY, Oct. 13, 1861. He died at home Nov. 29, 1861.
Sometimes the name appears as 'Stayton' in the military records. Captain Felix J. Staton's name is indexed that way as Captain of Co. "B", 3rd Kentucky Regiment. He resigned his commission due to ill health on Jan. 8, 1863. He's the closest we will come to a Kentucky officer by this name.
Apparently Joseph P. Staton never applied for a pension as a Confederate veteran. That suggests that he may not have had a basis for making a claim to be a Confederate veteran. A different man by this name served as 2nd Lieutenant of Co. "A", Woodward's Kentucky Cavalry. He died of wounds at Jackson TN in February of 1863.