The unsourced FindAGrave entry has Vernonburg, Chatham County, Georgia. This location did not exist until 1866.
William was born after 1746. He passed away after 1811.
Sources
Find a Grave, database and images (https://www.findagrave.com/memorial/182423499/william-burckhalter: accessed 11 January 2023), memorial page for PVT William Burckhalter (1745–1811), Find a Grave Memorial ID 182423499, citing Burckhalter Family, Monticello, Jasper County, Georgia, USA; Maintained by Lewie Dunn (contributor 47860774).
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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: