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Can you share a copy of the 1899 marriage record?
If Patrick was 36 in 1901 then he would have been born around 1865 rather than 1875.
I located a civil birth record and related baptismal record for a Patrick Burke with father Thomas Burke and mother Mary Kelly in 1866 which would match the age 36 in 1901. However, where the family lived was much further south in Co. Galway down by Loughrea. Possibly they moved north later. Please review the two records below and see if you think they are for your Patrick. Did he have siblings?
Name:Patrick BurkeDate of Birth:28-Feb-1866
Date of Baptism:29-Feb-1866Address:Not RecordedParish/District:KILLEENADEEMAGender:
Father:Burke ThomasMother:Kelly MaryOccupation:Not Recorded
Sponsor 1 /
Informant 1:Callagy MichaelSponsor 2 /
Informant 2:Callagy Bridget