In the 1850 and 1860 censuses, his given name was recorded as Madison, but in later records as Matthew, Mathew, Mat or Matt. It is likely that these all represent one name that went through the transformation Madison -> Mat -> Matthew, since Mat(t) is a nickname for both. But for ease of indexing, I’ve just put all the variations in his given name field.

Possibly a descendant of Samuel (b. ca 1755 in Pennsylvania) and Rachel Pettit of Greenup Co., Kentucky (linked in this database as a tentative brother of my Revolutionary War ancestor Matthew Pettit.) Many of their descendants moved to the border counties of southeast Ohio (Adams, Scioto, Athens and Lawrence) in the 1830’s, and then back to northeast Kentucky or West Virginia in the 1870’s to early 1900’s.

I cannot find a good match for Mat in any census earlier than 1880.

1880 census of Greenup Co., Kentucky, precinct 1, enumerated 21 June, lists on p. 66 as household #371/373:
McKee, Eliza, 38, single, keeps house, b. Penn Ireland Ireland. Gallaher, Easter, 36, sister, widowed, b. Penn Scotland Ireland. Carrignton, George, servant, farm hand, b. Ky - -. Petitt, Mat, 30, boarder, single, collier, b. Ohio Ohio Ohio. Grubb, John, 25, boarder, single, collier, b. Ky - -. Coffee, Thomas, 25, boarder, single, collier, b. Ky Ky Ky.

Her death certificate records Arizona Petitt, age 86, born 3 Mar 1868 in Kentucky, died 1 Feb 1955 in Winona, Fayette Co., West Virginia, widowed, father Thomas Davis, mother’s maiden name Mary Mann, cause of death hypertension, informant Charles Pettit, burial in Morris Creek Cemetery. (The two different spellings of Petitt/Pettit are not a typo, at least not on my part.)

1920 census of Kanawha Co., West Virginia, Cabin Creek district, enumerated 5 Jan, lists on p. 5A as family #1:
Locus, Pete, 56, b. Ky Ky Ky, in pour howse; Arzonie, wife, 52, b. Ohio Ohio Ohio. Pettit, Franklin, stepson, 32, single, b. Ky Ky Ky, miner; Grant, stepson, 17; Charlie, stepson, 15; George, stepson, 11. The three teen stepsons are listed as born WVa WVa WVa, but the parent birthplaces are wrong.

She is recorded twice in the 1930 census, once with her daughter Rosa, and once as a boarder with an apparently unrelated Vance family:

1930 census of Kanawha Co., West Virginia, Cabin Creek district, enumerated 1 May, lists on p. 32A as family #566/606:
Dooley, William M., 38, age at first marriage 20, b. Ky Ohio Ky, coal miner; Rosa L., wife, 34, age at first marriage 15, b. Ky Ohio Ohio; Virgie M., dau, 14, b. Ky Ky Ky; William F., son, 10, b. WV Ky Ky; Dorotha L., dau, 4 6/12, b. WV Ky Ky. Pettit, Arizona, mother-in-law, 61, widowed, age at first marriage 19, b. Ohio Ohio Ohio.

1930 census of Kanawha Co., West Virginia, Cabin Creek district, Union Mines, enumerated 8 April, lists on p. 9A as family #187:
Vance, Melvin, 44, age at first marriage 18, laborer at coal mines; Mabel, wife, 22; John, son 3 9/12. All born WVa WVa WVa. Petet, Arizona, lodger, 61, widowed, b. Ohio Ohio Ohio.

In 1940 she is recorded with her youngest son George and his wife Lena as Arizona Petitt, mother, 71, widowed, b. Ohio, living in rural Fayette Co., WVa in 1935.

Greenup Co., Kentucky marriage records list the marriage on 26 Mar 1885 of Mathew Pettet and Arizona Davis.

1900 census of Kanawha Co., West Virginia, Cabin Creek district, enumerated 15 June, lists on p. 19B as family #363:
Pettit, Matthew, 53, b. Aug 1846, Ohio Penn Ohio, coal miner; Arazone, wife, 34, b. Mar 1866, Ohio Ohio Ohio, married 18 years, mother of 7 children, 6 living; Benjamin, son, 14, b. Mar 1886; Mary, dau, 12, b. Nov 1887; Eliza, dau, 9, b. Jan 1891; Rosa, dau, 6, b. Apr 1894; Gracie, dau, 2, b. June 1897; Denver, son, 5/12, b. Nov 1899. All children born Ky Ohio Ohio.

1910 census of Kanawha Co., West Virginia, Cabin Creek district, Sharon village, enumerated 26 April, lists on p. 13B as family #237/239:
Pettit, Mathew, 62, b. Ohio Ohio Ohio, coal miner; Arizona, wife, 44, b. Ohio Ohio Ohio, first marriage for both, married 25 years, mother of 10 children, 9 living; Benjamin, son, 24, coal miner; Eliza, dau, 17; Rosie, dau, 15; Gracie, dau, 14; Denver, son, 12; Grant, son, 9; Charles, son, 5; George, son, 1 8/12. The three youngest boys born WVa Ohio Ohio, the older children born Ky Ohio Ohio.

Their daughter Mary Jane is listed two households below with her husband Hilda Thompson.

In 1920 Arizona and four of their sons are recorded with her second husband Pete Lucas, see her census notes.