He is mentioned in his daughter Mary's death record.
Names as they appear in Daughters Death Record, click for larger Image.
Birth year may be misattributed to this fella who died in Ireland. “Ireland, Civil Registration Indexes 1845–1958,” Index. FamilySearch, Salt Lake City, Utah. General Register Office. "Quarterly Returns of Births in Ireland with Index to Births." Belfast, Ireland.
The Gaston family look to be from Bellymena. The gentleman above could be a cousin or some other relation. They were Presbyterian. The assertion that they were from Carrickfergus is probably tied to the port from which they sailed to North America.
Ancestry User Paigepc44 has a profile for this William with this Census entry: Ancestry.com She also provides son Moses DEath Record which lists parent POB as Belfast.
Son - Moses, b 1819 in Pugwash, Cumberland County, Nova Scotia Moses profile on Geni. Moses GASTON was born around 1819 in Pugwash, Nova Scotia, Canada, the son of William and Mary Molly (Redmond) GASTON. Moses' parents were born in Ireland, so Moses was first-generation Canadian..Find A Grave: Memorial #55278903
Sons, Andrew, 1819 and John 1820, Traveled with Parents from Ireland - shipwreck on NS? Mary Margaret (aka) Molly Redmond, daughter of a Moses & Rebecca (Dunn) Redmond.Genealogy.com
Ancestry.com Message boards - Has William who married Mary Redmond being b. 1831 - Son/grandson instead? Also Lists a Hugh born in 1839 - possibly Grandson/son?
No direct evidence to support the theory - but could this be the grandparents/great grands? RootsChat
DNA match, Chromosome 9, 13.76 cM, to the Gaston's of Ballymena and to Jean Gaston, 1600 Carrickfergus, Ireland-1670, Carrenleagh, Cloughwater, Ireland and Agnes Navarre, 1615-1650 < John Gaston, 1645-107 and Esther Naugh < Hugh Gaston, 1687, Bellymena -1772 New Jersey. Is this connection a good connection or a collateral connection from somewhere else in these Limbs?
↑ "Massachusetts Deaths, 1841-1915," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:N75V-NNS : accessed 27 January 2016), John H. Lorman in entry for Mary A. Lorman, 27 May 1886; citing Lowell, Massachusetts, v 374 p 123, State Archives, Boston; FHL microfilm 960,232.
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It may be possible to confirm family relationships with William 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 (beta) of DNA with William: