There is no evidence relative to the existence of a son named John. However, the 1800 and 1810 censuses suggest that Hans Michael Carl had a son born in the late 1780s. His name might have been John. His mother might have been the second wife.
Sources
WikiTree profile Charles-421 created through the import of Coley Wolford Stayton McCarroll Bond.ged on Aug 7, 2011 by Tom Coley. See the Changes page for the details of edits by Tom and others.
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DNA Connections
It may be possible to confirm family relationships with John by comparing test results with other carriers of his ancestors' Y-chromosome or 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 John: