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The baptismal records for Kilmacteige RC parish start in April 1845 and marriages in 1848. I searched the subscription site Roots Ireland and did not find a baptismal record for a Michael Burke with father Garrett. Likely he was born pre-April 1845. I did not find any other children of Garrett Burke. He is listed in Gortemone in the 1858 Griffiths Valuation survey 9listed as Garrett Bourke).
Here is a web site devoted to Kilmacteige parish and possibly you will find some useful information. https://kilmacteige.com/2016/08/kilmactigue-and-kilmactiege-parish-churchwebsite-is-online/