First, I found some more info on Joseph Callahan and his wife Nancy They had a daughter Linda who married Jeremiah Sparks in Mitchell, North Carolina, son of Sam and Polly Sparks.
mentioned in the record of Jeremiah Sparks and Linda Calahan
Other information in the record of Jeremiah Sparks and Linda Calahan
from North Carolina Marriages
"North Carolina Marriages, 1759-1979," database, FamilySearch(https://familysearch.org/ark:/61903/1:1:F8WJ-3P5 : accessed 25 November 2015), Jos. Calahan in entry for Jeremiah Sparks and Linda Calahan, 14 Jun 1869; citing Mitchell, North Carolina, reference Vol 1 1870-1889; FHL microfilm 847,701.
Secondly, I find no connection between Joel and North Carolina except his military service. Joseph was born in North Carolina.. The two other siblings of Joseph do not support Joseph's lineage as being one their own. John Callahan was born in South Carolina and Catherine was born in South Carolina. And you have not shown any relationship between them and your Joel or to Joseph. Henry Callahan's wife was married in North Carolina. I understand that the Carolinas were all one in the time before the revolution but you have shown no evidence that ties Joseph to Joel. The fact that we could say the same for Henry does not help Joel's case. Henry shows a good case that he always lived in North Carolina. I have reviewed this case using mostly the evidence you presented and added little to the evidence you already know. My conclusion is that there is no case proving either man as his father. Hope this helps you. Wishing you good luck. David T. Robertson Robertson-7481.