Vicki, Company E of the 14th originated in Marion County and at least one adjacent county (Newton). In the 1860 census, Zachariah and John A. Beckham appear in Newton County (Zachariah was John’s father). Your man might be the Joseph “Beckum” listed in Marion County. Members of the household were: Joseph Beckum, head, age 29, farmer, born in NC - Rebecca, age 24, born TN - James, age 3, born AR - Sarah M., age 5 months, born AR

Source:
Joseph Beckum household, 1860 U.S. Census, Prairie TWP, Marion County, Arkansas Population Schedule, page 35, stamped page 365, lines 34-37, dwelling 243, no family #, National Archives Micropublication M653, roll 46.