On the 1830 & 1840 Censuses, there is only one male child that's unaccounted for. Born between 1826 & 1830. If Elizabeth was William's mother, this son would most likely have been William.
On the 1820 Census, there is one male child unaccounted for in Samuel's household that was born between 1811 & 1820. This child does not appear on any other census. This could likely have been George. He could have possibly passed away before the next Census. If it was, then his mother would have been Martha.
Sources
FamilySearch.com
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DNA Connections
It may be possible to confirm family relationships with George 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: