Jas Carmichael's purported birth date of 1815 or earlier is based on his four purported children, the first of which was born 1833 per available records.
FamilySearch as of August 2019 gives us the following:
Spouse: E (possibly Elizabeth) 1805–Deceased
Children:
Martha E Carmichael, 1833–Deceased, married Samuel Christian
Sarah Alabama Carmichael, 1835–Deceased, married Armand LeFils
Emeline T. Carmichael, 1842–Deceased, married Dan Lowe
Mary Arkansas Carmichael, Deceased
DNA matches exist between one descendant of Sarah Alabama Carmichael and two separate descendants of Emeline Carmichael.
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DNA Connections
It may be possible to confirm family relationships with Jas by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Jas: