Thomas was the son of Moses Ball Jr. and Mary Ann Hardin. He married Rachel Kelly (daughter of Jonathan Kelly and Patience Spencer) on 9 Mar 1820 in Harlan County, Kentucky. They were still living there in 1840. They had children (The first source below lists them as):

Isaac (m. twice)
Jonathan Kelly (m. twice)
Wesley (m. Mary Ann Jones)
Mary Margaret (m. James Madison Thomas)
Susannah (m. Alfred Williams)
Jesse (b. abt. 1833 d. unmarried)
Thomas J. (m. Mrs. Nancy (Hall) Price)
William (m. Hannah J. Marion)
Rebecca Jane (m. William Martin Quillen)
Harriett (m. Larkin Foley)

The second source below lists their children on pg 9 as:

Isaac
Jonathan Kelly Ball
Sooky (m. Alfred Williams)
Mary Ann (m. Madison Thomas)
Wesley Ball
Thomas (m. Nancy Price nee' Hall)
Jesse (died unmarried)
William (m. Hannah Marion)
Rebecca (m. Martin Quillen)

Sources:

"The Ball Family of the Potomac (1654-2004)" by Doris LeClerc Ball, PH.D. and George L. Ball, M.S.

"The Ball Family of Southwest Virginia" by Palmer R. Ball (1933)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ancestral File

name: Thomas H. BALL
gender: Male
birth: 1785
Fairfax, Fairfax, Virginia
death: 12 Apr 1856
afn: 3WZK-NQ
Parents
father: Moses BALL ;JR. (AFN: 1W3B-B9 )
mother: Mary Ann HARDIN (AFN: 3WZJ-D7 )
Marriages (2)
spouse 1: Rachel KELLY (AFN: CFP1-JB )
marriage: 9 Mar 1820
Fairfax, Fairfax, Virginia
children (11)

child 1: Wesley BALL (AFN: PNQV-RW )
gender: Male
birth 1830
, , Tennessee

child 2: Jessie BALL (AFN: PNQV-T8 )
gender: Male
birth 1834
Of Fairfax, Fairfax, Virginia
death Dead

child 3: Sookie BALL (AFN: PNQZ-DF )
gender: Female
birth 1826
, , Tennessee

child 4: Mary Ann BALL (AFN: PNQZ-GR )
gender: Female
birth 1828
Of Fairfax, Fairfax, Virginia
death Dead

child 5: Mary Ann BALL (AFN: 1DWX-MXK )
gender: Female
birth 1818
, , Tennessee

child 6: Sarah Or Sooky BALL (AFN: 1Z7T-4C5 )
gender: Female
birth Abt 1826
Of Fairfax, Fairfax, Virginia
death Dead

child 7: Jonathan Kelly BALL (AFN: PNQZ-RB )
gender: Male
birth 2 May 1824
, Lee Co., Virginia
death 1877

child 8: Isaac BALL (AFN: 1TR9-LG )
gender: Male
birth 1821
, Lee, VA
death , Lee, VA

child 9: Rebecca BALL (AFN: PNQZ-NS )
gender: Female
birth 1838
Of Fairfax, Fairfax, Virginia
death Dead

child 10: William BALL (AFN: PNQZ-K9 )
gender: Male
birth 1836
Of Fairfax, Fairfax, Virginia
death Dead

child 11: Thomas BALL ;[Jr.] (AFN: PNQZ-HX )
gender: Male
birth 1832
Of Fairfax, Fairfax, Virginia
death Dead

spouse 2: Rachel KELLY (AFN: 3WZL-59 )
marriage: 9 Mar 1820
Harlan Co., KY
children (9)

child 1: Rebecca BALL (AFN: PNQZ-NS )
gender: Female
birth 1838
Of Fairfax, Fairfax, Virginia
death Dead

child 2: Wesley BALL (AFN: PNQV-RW )
gender: Male
birth 1830
, , Tennessee

child 3: Sarah Or Sooky BALL (AFN: 1Z7T-4C5 )
gender: Female
birth Abt 1826
Of Fairfax, Fairfax, Virginia
death Dead

child 4: Jonathan Kelly BALL (AFN: PNQZ-RB )
gender: Male
birth 2 May 1824
, Lee Co., Virginia
death 1877

child 5: Isaac BALL (AFN: 1TR9-LG )
gender: Male
birth 1821
, Lee, VA
death , Lee, VA

child 6: Jessie BALL (AFN: PNQV-T8 )
gender: Male
birth 1834
Of Fairfax, Fairfax, Virginia
death Dead

child 7: William BALL (AFN: PNQZ-K9 )
gender: Male
birth 1836
Of Fairfax, Fairfax, Virginia
death Dead

child 8: Thomas BALL ;[Jr.] (AFN: PNQZ-HX )
gender: Male
birth 1832
Of Fairfax, Fairfax, Virginia
death Dead

child 9: Mary Ann BALL (AFN: PNQZ-GR )
gender: Female
birth 1828
Of Fairfax, Fairfax, Virginia
death Dead

Submitters (6)
submitter: aeball3379816
submitter: eimainsworth875564
submitter: sgsmith1281456
submitter: mrspencer2523488
submitter: drobbins547456
submitter: mdbeard585028

microfilm: 1394248
submission: AF83-056401

microfilm: 1394028
submission: AF83-005303

Notes
This person's information was combined while in Ancestral File. The following submitters of the information may or may not agree with the combining of the information: DELAPHINE/ROBBINS/ (2067844) MARVA DIANE/BEARD/ (2113707) A ELDEN/BALL/ (2181145) STANLEY GORDON/SMITH/ (2486258) MANUEL R./SPENCER/ (2523488)

Source Citation
"Ancestral File v4.19," database, FamilySearch, entry for Thomas H. BALL.