the book, The Descendants of Aquilla Greer, Sr. 1719-1790, lists William as a son, however, they know nothing more about him.
The marriage record of his parents in Baltimore County Maryland 1737, and he was born circa 1742. The Land Records indicate that the family was still living in Maryland until after 1777. So, I believe we can assume he was born in Baltimore, Maryland.
The other known children were born, "St. John’s and St. George’s P. E. Church, Baltimore and Harford Parish Registers, 1696-1851; p. 180, Lowraner Greer Daughter of Moses Greer & Mary his wife Born June 7th 1757; p. 180,"
Williams' parents, Moses & Mary Bayley married in January 1737 in Baltimore County, Maryland. This is most likely also where William was born. [citation needed]
Siblings
this is a "possible" list of children
James Greer, born about 1733
William Greer, born about 1742
Moses Greer, born 9 September 1755, Baltimore Co.
Lowraner Greer (daughter), born 7 Jan 1757, Baltimore Co., died 1759?
Aquilla Greer, born 9 September 1760, Baltimore Co.
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DNA Connections
It may be possible to confirm family relationships with William by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: