The Civil War Pension Index has a file for Smith P. Ham, filed on 19 Oct 1882 for an invalid pension, service in the Ky 23 Infantry, application number 462844. On July 28, 1903 Martha A. Ham filed for a widow’s pension, application #788650. (The index shows only the file card, with no details.)

1860 census of Fleming Co., Ky, district 2, Flemingsburg P.O., enumerated 31 July, lists on p. 61 as family #417/482:
Smith T. Ham, 26, laborer; Martha A., 26; John P., 8; Emily R., 2. All born in Kentucky.

I cannot find this family in the 1870 census.

1880 census of Rowan Co., Ky, Pine Grove precinct, enumerated 4 June, lists on p. 27 as family #195/212:
Ham, Smith P., 49, farmer; Martha A., wife; Martha J., dau, 17; Mary A., 12, dau; Ida V., 8, dau; Laura E., 6, dau. All born Ky Ky Ky.

The preceding household is that of their son John.

1900 census of Rowan Co., Ky, Pine Grove precinct, enumerated 12 June, lists on p. 10A as family #169:
Ham, Smith, 69, b. Jan 1831, farmer; Martha A., wife, 69, b. Feb 1831, married 48 years, mother of 9 children, 6 living; Thurman, Martha, dau, 37, b. Feb 1863, widowed; Wm R., grandson, 3, b. Oct 1896; Bays, Otha S., grandson, 14, b. Apr 1886. All born Ky Ky Ky.

The next household is headed by their son John.