Do you know religious denomination?
R.C. parish registers on National Library of Ireland website:
R.C. parish of Tynagh, Diocese of Clonfert
https://registers.nli.ie/parishes/0339Loughrea R.C. parish
https://registers.nli.ie/parishes/0336Click on links under "more information" to see if there are registers for additional years.
Leitrim R.C. parish is between Tynagh and Loughrea parishes.
Church of Ireland registers exist for Loughrea from 1747.
How did you calculate 1803 as Ned Naughton's year of birth?
Have you found transportation or other convict records for him? When was he transported?
Was Ned single or married at the time of transportation? Did he marry afterwards?