Michele,
The name McBarron is not too common in Fermanagh. In Griffiths Valuation (1862) there were just 24 households listed, in the parishes of Kinawley, Aghavea, Aghalurcher, Derryvullan, Enniskillen and Cleenish. It was most common in Kinawley (16 households).
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
Church records can sometimes be a way of confirming a person’s baptism and parents but none of those 6 RC parishes has any records for 1827 or earlier. Kinawley, Aghalurcher and Cleenish all start in 1835, the rest later.
A small portion of the 1821 census of Fermanagh has survived. There is one Patt McBaron in it, but he is only 18 years old, so not your family.
http://www.census.nationalarchives.ie/pages/1821/Fermanagh/Aghalurcher/Carrahoney/12/
Tracing your family may be very difficult due to the general lack of records for the period you need.