Have you seen this: https://www.familysearch.org/tree/person/details/L6T2-3Y5
Priscilla L Harrison dau of Isham Harrison, married a Puckett, and had son Alfred H Puckett. Her approx birth year of 1798 appears incorrect; she was probably about 12 years older. I don't know the documentation for any of this.
Douglass Josephus Puckett was from (I think) Laurens Co, SC. He was an attorney in the town of Spartanburg, Spartanburg Co, SC. Deed records show that Isham Harrison sold land to Douglass Josephus Puckett in Spartanburg Co in 1808. When Douglass Josephus Puckett sold land in Spartanburg in 1811, his wife was listed as Priscilla L Puckett. Isham Harrison died in Missouri in 1835.
Charles Puckett, son of the first Douglass Puckett, came to SC and settled near Musgrove Mills on the Enoree River in what later became Laurens Co, SC. He was there by 1777. I think his younger brother Douglass Puckett Jr joined him. If you go to the SC Archives online, you can search for Charles Puckett (https://www.archivesindex.sc.gov), he is indexed as "Pucket, Charles". There is a plat for Ann Musgrove showing both Charles Pucket and Douglass Pucket as adjacent landowners.
I think both Charles and Douglass had sons named Douglass - Charles had Douglass Josephus Puckett and Douglass had Douglass Josiah Puckett (I think, I may have them backwards). Both D J Pucketts were lawyers and they frequently used their full names in records, probably to tell them apart.
I am working on this slowly: https://sites.google.com/site/womackgen/puckett-family/d12-douglass-puckett?authuser=0
The Puckett lines in Laurens Co, SC are complex, and I am trying to sort them out.
Note also a Cheatham connection - Charles Puckett had a brother and a son named Cheatham Puckett. Isham Harrison's wife's mother was a Cheatham according to the link above.
I found a little more, some nice person on ancestry added this record:
Missouri State Archives, Jefferson City
Madison County Probate Estate File
Reel C7777
Estate of Isham Harrison
Amey Harrison & Caleb Cox
To Application for Letters of Adm
Clerk of Madison County Court
Filed March 9th 1836
Wm M. Newberry clk
State of Missouri
Madison County
County Court, Clerk’s office, in vacation, March the 9th 1836
Be it Remembered, that on this 9th day of March, in the year of our Lord eighteen hundred and thirty six, before me, the undersigned, Clerk of the county court of Madison County, came Amey Harrison and Caleb Cox, and made application for Letters of Administration on the estate of Isham Harrison deceased, late of said county, and ____ [?] to law make oath and say, that the said Amey Harrison widow of said deceased, Nancy Powell, late Nancy Harrison, George H. Miller, Amey M. Miller, Elizabeth C. Miller, Eliza W. Miller, Sarah Jane Miller, John I. Miller & Nancy C. Miller infant children of Sarah D. Miller decd, late Sarah [referred to as Sally on another document] D. Harrison all of the said County of Madison – Damascus T. Allen, Minerva Long, late Minerva Allen, Vermont R. Allen, Napoleon C. Allen, Eugene N. Allen, Harriet Allen, Musadore E. Allen, children and heirs of Elizabeth Allen decd, late Elizabeth Harrison, all of said county, Andrew M. Harrison, Lemuel R. Harrison and Lucy Goode, late Lucy Harrison, of Franklin County State of Illinois, and Alfred H. Pucket and Eliza W. Thompson, late Eliza W. Pucket, of the county of Perry and State of Missouri – and Ethelred [?] B. Puckett whose residence is not known), children and heirs of Priscilla L. Pucket, late Priscilla L. Harrison, are the only heirs and legal representatives of the said Isham Harrison deceased, so far as the said applicants know and believe; and that the said deceased died without a will, so far as said applicants know and believe. And that they will make a perfect inventory of, and faithfully administer, all the estate of the deceased, and pay the debts as far as the assets will extend and the law direct, and account for and pay all assets which shall come to their possession or knowledge.
Amey Harrison
Caleb Cox
Sworn & Subscribed to before me, this 9th day of March, A.D., 1836.
William N. Newberry clerk