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I searched on the subscription site Roots Ireland and did not find a Peter Fadden baptismal record in Co. Mayo around 1847. Ballyhean would be part of the RC parish of Castlebar and baptismal records are available starting in 1838 https://registers.nli.ie/parishes/1039 so maybe the Faddens were from a neighboring parish which does not have records back to 1847.
I looked at the 1855 Griffiths Valuation head of household listing and there was a Michael Fadden in Cloonaghmore townland. Possibly this record was for the father of Peter? https://www.failteromhat.com/griffiths/mayo/ballyhean.htm
I looked at the 1901 census and there was a Michael Fadden listed with his wife Mary and son Henry in Cloonaghmore. His age was shown as 74 but likely understated. Possibly this is the same Michael shown in the Griffiths. http://www.census.nationalarchives.ie/pages/1901/Mayo/Ballyhean/Cloonaghmore/1583504/ In the 1911 census, Michael was deceased, Henry was married and his mother Mary was living. http://www.census.nationalarchives.ie/pages/1911/Mayo/Ballyhean/Cloonaghmore/712573/
Michael Fadden died in 1905 at age 85 https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1905/05584/4568567.pdf