Ancestry.com "Kentucky Marriages to 1850" has marriage listed twice, onceas Anthony Peyton and once as Joseph Peyton.
Ancestry World Tree in Database 1866988 has Anthony's mother as his father's other wife, Elizabeth Olwel.
"Paton" in 1850 census.
Could not find Anthony Payton (or Peyton) in 1820 census in Kentucky. There is an Anthony Payton in Westmoreland Co., Virginia but this appears to be an older man. He could be Joseph in 1820 census (see marriage note above).
BIOGRAPHY: Land patent issued January 3, 1832 for 69.56 acres in Parke Co. (BLM Document Nr. 14470, Accession/Serial Nr. IN1160_.174.
Barbara Carter - On July 1, 1831 purchased 6 acres at W1/2 SW1/4.
(Account from 1893) Anthony was born in the Old Dominion (Virginia) in 1801, and removed with his parents to Kentucky in his early youth. (Lived in Mason County.) In that state he married Miss Margaret, daughter of Mark Wallingford, who was an early settler of the Blue Grass region. To this worthy couple were born four children while in Kentucky, and in 1828 the family removed to Indiana, settling in Greene Township, Parke County, on section 22, where his the father (referring to Anthony) rented a farm for four years. In 1831 he located near Bellmore, in Union Township, where he entered land. He was one of the first settlers of the township, and he at once commenced piling brush and clearing a place to raise food for his family, and so diligently did he work that before the spring had passed five acres were ready for seed. Six children were born to Mr. and Mrs. Payton in this county. Only four of the family now living, viz.: Mrs. Julia Lewis of Sullivan County, Ind.; James. F., a resident of Greene Township; John L., of Sullivan County, Ind., and our subject (Thomas). Anthony, who was a member of Predestinarian Baptist Church (Mount Moriah), died October, 1853. His wife, who held the same faith, survived her husband nearly half a century, her death occuring in December, 1882. Mr. Payton was a strong Democrat, and was actively interested in the welfare of this region, to the development of which he contributed in no small measure.
1850 census: Farmer with real estate of $1,200.
DEATH: Will:
I, Anthony Payton, of the County of Parke in the State of Indiana do make and publish this my last will and testament hereby revoking and making void all former wills by me at any time heretofore made. First, I direct that my body be decently intered and as to such worldly Estate as it has pleased God to entrust me with, I dispose of the same in the following manner (to wit): I direct that all my just debts and funeral expenses be first paid. I further direct that my wife, Margaret Payton, shall have possession of the farm in which I now reside and also the personal property and the profits of the same for the support of herself and the three children that are now at home as long as hse remains my widow. I direct that Laureny Douglass, John L. Payton and Harvy Payton to have a good common education and I direct that said Laureny, John and Harvy shall have as good setting out as I have given my other children. I direct that my son James Payton to be my Executor, and further I direct that said James to superintend the farm and to manage the business for my family, and in case of his death or inability to do so then and in that case, I direct my son Thomas to take charge and manage for the family as James is directed to do, taking receipts for all money paid out so that it may be satisfactory to the family, and also keep an account of all moneys paid to him for the benefit of my family, and I further direct that said James or said Thomas to be paid a reasonable compensation for their services out of the profits of my Estate and at the death of my wife Margaret, I direct that all my property and Estate to be equally divided among all my children share and share alike whose names are Julina, William, James, Mary, Thomas, Laureny, Douglass, John L. and Harvy, and I further direct that my farm shall not be sold or divided until the youngest child arrives at the age of twenty years, provided however if a majority of my children that is twenty one years old shall be in favor of selling then in in that case I direct that my farm may be sold. In testimony whereof I, Anthony Payton, the testator have hereunto set my hand and seal this twelfth (12th) day of August in the year of our Lord, one thousand eight hundred and fifty three (1853). (Witnessed by Jesse Maticks and Zebulon Collings and delivered to probate by them on November 22, 1853.)