Based on the 1850 Census show below she was born about 1783. She was the daughter of John Barnes and Ruth Fisher. She passed away in 1822.
Sources
"North Carolina, County Marriages, 1762-1979 ," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XF9P-LLZ : 3 November 2017), Caga Fortner and Elisabeth Barns, 05 Feb 1807; citing Wilkes, North Carolina, United States, p. , Office of Archives and History, Division of Archives and Records. State Archive of North Carolina and various county Register of Deeds; FHL microfilm 546,477.
"United States Census, 1830," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XHGG-GRN : 24 August 2017), Elizabeth Fortner, Allen, Kentucky, United States; citing 57, NARA microfilm publication M19, (Washington D.C.: National Archives and Records Administration, n.d.), roll 33; FHL microfilm 7,812. Allen County created from Warren County
"United States Census, 1840," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XHTP-HJR : 15 August 2017), Elizabeth Fortner, Simpson, Kentucky, United States; citing p. 199, NARA microfilm publication M704, (Washington D.C.: National Archives and Records Administration, n.d.), roll 124; FHL microfilm 7,832. Simpson County created from Allen, Logan and Warren Counties
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M658-X27 : 12 April 2016), Elizabeth Fortner in household of Alexr Fortner, Lawrence county, part of, Lawrence, Kentucky, United States; citing family 472, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.). Living with son Alexander
Created by Will of father John
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DNA Connections
It may be possible to confirm family relationships with Elizabeth by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Elizabeth: