The Tithe Applotments (1820s-1830s) would be closest record to your ancestor John Hagan's life time and his emigration/naturalization date of 1838. The full tithe records didn't survive for Donaghedy parish, but you should check for Hagan/O'Hagan throughout County Tyrone, to see where families of that surname DID live in the 1820s-1830s. Even if you don't know your ancestor John Hagan's religious denomination, if he named his children given names like Daniel, Patrick, Bridget, Brian, Connor, etc., he was almost certainly Roman Catholic. Protestants didn't give children Irish names like those, particularly Catholic saints' names. If possible, you should try to follow up on Len's suggestion about church records. County Tyrone has over 2100 townlands, dozens of which begin with "B- ". A longer name might have been shortened (verbally) to sound like Barnen, as Len pointed out, and it didn't necessarily begin with "Bar- " but may have been "Ber- " or "Bor- ". This is an excellent townlands database: https://www.townlands.ie/ And the very helpful IreAtlas Townland database: https://thecore.com/seanruad/ The Place Names database at Queen's University is great, though still a continual work-in-progress: https://www.ulsterplacenamesociety.org/the-project Then there's the Place Names of Ireland database: https://www.logainm.ie/en/ There are probably more clues tucked away in family data that you already have. Whom did John Hagan marry, and when? Do you know her home origin? Was her surname associated with a place where there were Hagans in County Tyrone, such as in the Tithes? On DNA, did a direct male descendant of John Hagan take the Y-DNA test (for males only), and compare his test results with other Hagans for paternal origins? If you're only going by autosomal DNA test results (the test offered by Ancestry.com, My Heritage, 23-&-Me and other companies), you won't get the same kind of matches. Good luck with your search, Annie