as per the book "Notable Southern Families".
President James Knox Polk was born in North Carolina November 2 1795. He was the eldest son of Samuel Polk and Jane Knox Polk. When he was eleven years of age the family moved to what is now Maury Co TN. He went for his education to the University of North Carolina he graduated there in 1818, was admitted to the Bar in TN in 1820, and was elected to Congress in 1825. In 1835 he was elected Speaker of the House and held this office for five sessions. In 1839 he was elected Governor of TN . In 1844 he was elected Presendint of US. He married Miss Sarah Childress, but left no children. he died June 14 1849, and is buried in Nashville, TN. He left no children. (below is a list of his siblings and their spouses and issue as per book Notable Southern Families).
The children of Samuel Polk and Jane Knox Polk were:
James Knox Polk, Maria Polk; Marshall T. Polk; Eliza Polk; Franklin Polk; Samuel PolkJr, John Polk; Ophelia Polk; Naomi Polk, and William Polk.
Of these Marie Polk married ___Walker and had Samuel Walker; J. Knox Walker; Marshall Walker; Andrew Walker; Jane Walker who married a Burnett; Mary Walker who married a Pickett; Sarah Walker , who married a Green; James Walker unmarried, and Annie Walker who married a Phillips.)
Eliza Polk married a Caldwell of Richmond, and had two children, Samuel Caldwell and James Caldwell.
Naomi Polk married a Harris and had four children, Maria Harris , Malvina Harris, Laura Harris and Amelia Harris.
Ophelia Polk married a Hayes and had two children, Jenny Hayes and Naomi Hayes.
William Polk married and had three children, James K. Polk Jr, William Polk and Tasker Polk.
Franklin Polk died without issue,.
John Polk died without issue,
Samuel polk died without issue.
Marshall T. Polk had two children, Eunice and Marshall Tate Polk,Jr.
You may also like to know that the Progeniter of the Polk family is John Pollock, a gentleman of landed property near Glasgow. His son was Robert Pollock, who married Magdalen Tasker Porter, the daughter of Colonel Tasker, who was Robert Pollock's commander in Oliver Cromwell's Army. Robert Pollock in 1659 emigrated from Ireland to Maryland accompanied by his wife and children. It is about this date that "Polk" was evolved from Pollock.
Hope this helps.