His birth date according to the 1820 census would be between 1776 and 1794. It is unlikely he is Willoughby's father.
Sources
1820 Census: "1820 United States Federal Census" 1820 U S Census; Census Place: Williamsburg, South Carolina; Page: 303; NARA Roll: M33_120; Image: 384 Ancestry Sharing Link - Ancestry Record 7734 #978949 (accessed 12 May 2022) William Parker.
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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 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 of DNA with William: