Note - the date of birth is questionable - see Elizabeth b. 14 June 1706 married Ransford Avery. The Elizabeth that married Ransford is daughter of James Rogers.
Sources
James Rogers of New London CT and his descendants. J.S. Rogers 1902 pages 95-96, 222. Reprint 2012.
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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: