I know of no definitive documentation to prove Larkin Box's parentage, but I offer the following circumstantial evidence in a working hypothesis that Larkin Box was the eldest son of Stephen F. Box:
Ophelia Wade in her book, "The Box Book with McElroy and Floyd", covered Larkin Box but did not speculate as to who his father might be. However, Ophelia Wade had Josiah Box as the father of Robert, Henry, John W. and Hiram Box (sons) and Keziah Box (daughter). Later research has found that in error as the Caldwell family register from the family of Frances Box Caldwell had Blanton P., Frances, Reuben F., and Michael James as the children of Josiah and Mildred Powell Box and that has been confirmed in research by Verna Stone.

The circumstantial evidence at hand seems to suggest Stephen F. Box could have been the father of Larkin. The 1850 Maury Co. TN census indicates Larkin was born abt. 1799 in TN and had a son, named Stephen. Stephen F. Box who is being proposed as Larkin's father, was recorded in Smith Co. TN court minutes in 1799. Ophelia Wade records Stephen F. Box as having a son, James Box, born in 1801 in Smith Co. TN.

Larkin Box is recorded as marrying Frances Miles Nov. 14, 1820 in Blount Co. AL. Other children of Stephen F. Box were married in Blount Co. AL (Margaret Box m. in 1822, Dicy Box, m. in 1823 and John A. m. in 1825). Larkin Box was recorded in the 1830 census of Blount Co. as a close neighbor of Stephen Box. Larkin could have been an older son of Stephen F. Box as there appear to be 3 other sons of Stephen (James (b. 1801), John A. (b. 1803), and Stillwell (b. 1810) in the 1830 census of Blount Co. AL.

Ophelia Wade indicates all of Stephen F. Box's sons except the oldest, James Box, went to Texas with their father. James was enumerated in the 1850 census of Tishomingo Co. MS with a son named Stephen. However, if Larkin Box were the oldest son of Stephen F. Box, it seems he moved to Maury Co. TN to be with his wife's people and was enumerated in the 1850 census of Maury Co. TN with a son named Stephen, and was apparently buried in Gilliam Cemetery in Maury Co.