as documented in the BOX Book -
1810/20 Census in Laurens Co, So Carolina
1830 Census in Fayette Co, Alabama
1840 Census in Choctaw Co, Mississippi
1840/50/60/70/80 Census all BOX families in Choctaw Co, MS are his descendants.
5 children:
p.52.   I. Robert BOX b.1802-1804, d.>1840 prob. In Lincoln Co, Arkansas
p.56.  II. Henry BOX b.1804-1807 TN, d.>1860 m. Jane/Jincey b.TN
p.57. III. Dau. b.1800-1810 (maybe Keziah BOX who m. Simeon BRIGHT)
p.57.  IV. John W. BOX b.1800-1812 Ala, m. Nancy b.1838 GA
p.57.   V. Hiram BOX b.1813 Ala. (listed as deaf & dumb with brother John in 1860)

Josiah Box first appears in a census in the 1810 Census of Laurens Co. SC indicating he had a wife, two sons and a daughter. There is documentation that indicates his wife was Mildred “Milly” Powell and his children were Blanton P. Box, born Aug. 19, 1802, Frances F. Box, born July 30, 1805, and Reuben F. Box, born Dec. 8, 1807. In the 1830 census, Josiah was in Fayette Co. AL. Records show Josiah Box was involved in the Methodist Episcopal Mission for the Chickasaw Nation in the late 1830s, and he was counted in the 1840 Choctaw Co. MS Census. He died in 1844 and was buried in Greensboro, MS.
An extensive account of Josiah Box's son and daughter, Reuben Franklin Box and Frances Finney Box Caldwell, and their families can be found in The Box Family History, Reuben Franklin Box and his California Family by Alice Box Ramsay Akins. An e-book version is available on line at familysearch.org
Bio information courtesy of contributor #46996872 - Joseph Fox