Try the free search tool at https://familysearch.org/
Here are some likely candidates from that site. This Clara was b abt 1812-1813 in AL, parents both born in SC. Husband William C b abt 1803-1806 in TN, parent b VA.
If you plug in the various children's names from the census data, you may find out more and confirm that this is the correct Clara. For example, when plugging in Montgomery Bennett Thomas, there are several census that the location is: Kennamer, Wright, Marshall, Alabama - which means the township/area is named Kennamer - maybe after Clara's ancestors???
Happy hunting
ps Please not that when using family search - the pages note the citation to be used for that record at the bottom.
https://familysearch.org/
Alabama, Deaths, 1908-1974
https://familysearch.org/pal:/MM9.1.1/JDVK-PSH
Name: Robert J Thomas
Death 17 Oct 1918 death place: Woodville, Jackson, AL
Male White Married Farmer
Spouse Nancy Thomas
birth 19 Nov 1850 Columbus City, Marshal, Ala.
father William Thomas birthplace: VA
mother Clara Kennamer birthplace: Woodville, Jackson, Ala.
Alabama, Marriages
https://familysearch.org/pal:/MM9.1.1/FQW2-1Q5
groom Robert J. Thomas
bride Nancy L. Allison
marriage date: 05 Feb 1903
marriage place: Madison, Alabama
United States Census, 1880 Woodsville, Jackson, AL
https://familysearch.org/pal:/MM9.1.1/M4JL-86D
self W. C. Thomas M 75 b abt 1805 TN /VA/VA
wife C. Thomas F 68 b abt 1812 AL /SC/SC
son Geo. Thomas M 18 AL
United States Census, 1870 Woodsville, Jackson, AL
https://familysearch.org/pal:/MM9.3.1/TH-267-12056-199820-74?cc=1438024&wc=1592331
William C Thomas M 64y Tennessee
Clara Thomas F 57y Alabama
Robert Thomas M 19y Alabama
Montgomery B Thomas M 17y Alabama
William G Thomas M 15y Alabama
James H Thomas M 13y Alabama
Sarah A Thomas F 12y Alabama
Rebecca J Thomas F 10y Alabama
Sarah A Thomas F 19y Alabama
United States Census, 1850 Marshall county, Marshall, AL
https://familysearch.org/pal:/MM9.1.1/MH5Q-1Z4
William C Thomas M 44 Tennessee
Claracy Thomas F 33 Alabama
William L Thomas M 18 Alabama
James M Thomas M 14 Alabama
Nancy L Thomas F 12 Alabama
Isabel Thomas F 10 Alabama
Margarett L Thomas F 8 Alabama
David A Thomas M 5 Alabama
Joseph P Thomas M 2 Alabama
Another example from familysearch
Name Montgomery Bennett Thomas
death date 20 May 1921
death placeWoodville, Marshall, Alabama
gender Male
race (standardized)White
age at death68y 11d
birth date 09 May 1853
birthplace Woodwell, Ala.
marital status Widowed
spouse's name Martha Jane Thomas
father's name Wm. S. Thomas
occupation Farmer
cemetery Pisgah Cemetery
burial date 21 May 1921