Hi There
Just to clarify how I see your tree at present :
Matthew Thomas b 1795 Wales
(His parent's could have been Welsh and then for whatever reason emmigrated to Galway OR they could have been from Galway and had gone to Wales for a time, had Matthew and returned to Galway - either way that may never been known).
So, we know that in 1828 there was a Matthew Thomas in Kilcummin Galway and also a Patrick Thomas (this Patrick could have been either Matthew's father OR Matthew's brother).
We know that in 1832 Matthew Thomas married Mary Conway in Kilcummin Galway.
We know that Matthew and Mary had a son called Patrick whom was born about 1834 in Kilcummin (so was probably their first born child) - to clarify PATRICK MARRIED IN THE US as per the marriage that I sent you.
They had a son called John Thomas born 1843 Kilcummin (your GG Grandfather).
You now have an exact area in Knockilaree where the family were for a time.
Now, your issue is that Irish civil records only began in 1864 so you are lucky to have gotten the few church records that you have !
Kilcummin Church records are far and few between for that time.
You may pick up a few other bits and pieces of random info from this site !
https://familysearch.org/learn/wiki/en/Kilcummin_Civil_Parish,_County_GalwayTara