"Kentucky Births and Christenings, 1839-1960," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/FWJ8-S9G : accessed 1 February 2015), Martha Price in entry for Josiah Gastineau, 17 Oct 1854; citing Pulaski, Kentucky, reference yr 1854 p 4; FHL microfilm 216,838.
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DNA Connections
It may be possible to confirm family relationships with Josiah by comparing test results with other carriers of his ancestors' Y-chromosome or 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 Josiah: