Welcome to Ireland Reaching Out!
Unfortunately, the RC reocrds for Cootehall/Ardcarne parish do not begin until 1843. When I searched the subscription site Roots Ireland, I did not find any baptismal records for children of Thomas Fulton and Ann Roche. Below is a trancription of a likely baptismal record for Mary Fulton in Croghan parish.
You may want to add John's story to our XO Chronicles site https://irelandxo.com/ireland-xo/history-and-genealogy/ancestor-database
Name:Mary FultonDate of Birth:
Date of Baptism:26-Jan-1837Address:Not RecordedParish/District:CROGHANGender:FemaleCountyCo. Roscommon
Father:John FultonMother:Brigid CasyOccupation:
Sponsor 1 /
Informant 1:Patrick GoulrickSponsor 2 /
Informant 2:Anne Fulton