The only thing known at this time is the Johnson surname due to that of the location and birth of his son George. There are multiple "suspects" located in the birth area of George in Ohio...several of which could be his father, but the US Census does not give any clues.
Note HI1040(Research):Check of the 1830 US census for Licking County, Ohio finds a James Johnson age between 30 & 40 with a single son between 5 & 10 years old. There is also a Joseph Johnson age between 30 & 40 with a single son in the same age range. One other Johnson is John J, age between 60 and 70, who is most likely the father of the 2 younger Johnsons.
Sources
↑ Source: #S138 Page: Baltimore, ED 203, p. 13A, dwelling 69, family 74, George W. Johnson family; NARA microfilm publication T9, T9-1014. Quality or Certainty of Data: 3 Note: Gave fathers birth location as New Jersey
1880 U.S. census, Fairfield County, Ohio, population schedule, Baltimore, enumeration district (ED) 203, p. 13A, dwelling 69, family 74, George W. Johnson family; NARA microfilm publication T9, roll T9-1014.
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DNA Connections
It may be possible to confirm family relationships with Unknown 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 Unknown: