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The RC baptismal records for Stradbally RC parish start in November 1806 https://registers.nli.ie/parishes/1093 The subscription site Roots Ireland actually has Stradbally baptismal records back to 1797. I searched Roots Ireland for baptismal records where the father was John Dee in Stradbally and the earliest record was 1809.which would be too late for Nicholas if he emigrated in 1820. I did not see any records for Ned/Edward, Richard, Maurice, or Catherine. I did find a Margaret in 1813 which is below but no way of knowing if there is a connection to your family. I assume you do not have the mothers name?
You can add Nicholas' story to our XO Chronicles site and possibly someone will see a connection https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-data...
Have you considered DNA testing?
Name:Margaret DeeDate of Birth:
Date of Baptism:25-Apr-1813Address:
Father:John DeeMother:Honor CoffeeOccupation:
Sponsor 1 /
Informant 1:Edmund Hahesy Sponsor 2 /
Informant 2:Mary Thompson