The online birth records of the children of John and Rhoda stop at Mary in 1784 but this John and sister Rhoda are found in the baptism records. The birth records are from the Barbour Collection of Family Bible Records which is on microfilm at the Connecticut State Library.
Unsourced documents indicate he died in infancy.
Sources
Connecticut, Church Record Abstracts, 1630-1920, Volume 070 Part 2 Middletown, (ancestry.com)
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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.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: