Martin:
Welcome to Ireland Reaching Out!
I checked Roots Ireland from 1825-1835 and they did not have any baptismal records for a Thomas Molloy in Co. Mayo. Many Mayo RC parishes dod not have records back to 1830.
I assume Thomas emigrated. Have you located his parents names?
You may want to add his story to our XO Chronicles site https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-dat…
Have you considered autosomal DNA testing?
Roger McDonnell