The first child named Ebenezer Brown of Ebenezer and Margaret Brown died before the birth of their second child named Ebenezer on 5 May 1738.
Sources
"New Hampshire Birth Records, Early to 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FLL4-6M9 : 12 December 2014), Ebenezer Brown, 16 Nov 1726; citing Kensington, Rockingham, New Hampshire, United States, Bureau of Vital Records and Health Statistics, Concord; FHL microfilm 1,000,487.
Family Register of Ebenezer & Margaret Brown, NH Town Clerk, Kensington, Rockingham County, New Hampshire Town Records, Vol. 1, stamped page 325, familysearch.org image 167/206.
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DNA Connections
It may be possible to confirm family relationships with Ebenezer 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 Ebenezer: