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I checked Roots Ireland from 1853-1863 in Co. Armagh and the only Patrick Brady baptism with a father Michael is shown below. Civil registration of births did not start until 1864. I assume this is not your Michael??
Name:Patk BradyDate of Birth:
Date of Baptism:20-Mar-1857Address:
Father:Michael BradyMother:Ann MorganOccupation:
Sponsor 1 /
Informant 1:Patk McCaulSponsor 2 /
Informant 2:Ann Sherry