A number of unsourced family trees list the same 10 children (including two Agatha's, one born about 1796 and the other about 1812), but not necessarily in the same order. Some even list 4 additional children born after 1818, and one has those children with another wife. But there's no evidence that those children (or the other spouse) belong to Barnett's household (at least not indicated on the 1820 and 1830 census).
The US census from 1810 through 1830 seem to indicate 12 household members altogether of various ages. 9 in 1810, 9 also in 1820 but with 3 under 10, and only 8 in 1830. The family was living in Virgina in 1810, but in Tennessee for the 1820 and 1830 census.
One very credible source lists only 8 children (and only one Agatha, the early one), BlankenshipOrigins1.pdf by Don Blankenship and hosted on James Blankenship's website: http://www.blankenshipweb.com/ (Isham B./Thomas is also missing from his list). The 8 match the current links on Barnett's profile here, as of today.
But I can't help but wonder about the other 2 indicated on the census. And who do these other 4 belong to?[2]
Timeline
1810: living in Franklin county, Virginia with 9 household members (7 children; 2 boys; 5 girls) [3]
1 boy 16-25
1 boy, 1 girl 10-15
4 girls <10
1820: living in Smith county, Tennessee with 9 household members (7 children; 1 boys; 6 girls -- 3 new since 1810) [4]
2 girls 16-25
2 girls 10-15
2 girls, 1 boy <10
2 boys, 1 girl not at home
1830: living in Smith county, Tennessee with 8 household members (6 children; 1 boy; 5 girls) [5]
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DNA Connections
It may be possible to confirm family relationships with Barnabas by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
Frank Blankenship :
Family Tree DNA Y-DNA Test 111 markers, haplogroup R-FT48099, FTDNA kit #810240, MitoYDNA ID T16065[compare] +
Y-Chromosome Test, MitoYDNA ID T16065[compare]