There are three adjoining townlands in north Cork with Labbamolaga (in Irish, Leaba Molaga) in their names: Labbamolaga West, Labbamolaga Middle, and Labbamolaga East. All are in the ciivil parish of Templemolaga. Some info about Labbamolaga Middle can be found at this link (with links there to move on to info about the adjoining townlands:
Two, or perhaps all three of the townlands are in the Catholic parish of Kildorrery, and the Catholic parish registers for that parish are available back to 1803 for marriages and 1824 for baptisms, so you should be able to find some good info there, at this link: https://registers.nli.ie/parishes/0065
It's hard to tell from the maps involved, but it's possible that Labbamoraga East is in the next Catholic parish to the east, Mitchelstown. There is an interactive map at the above site there which will allow you to move on to that parish, in which the baptismal records go even further back.