Thanks for your reply. The Martin you have mentioned keeps popping up in my research, but I cannot find a connection. I have found a civil war record of my relative that mentions he is from Crossboyne. It was faded and the handwriting was difficult to understand but that appears to be the area. When Patrick Ansboura died in New Orleans, his elder son only stated he was from County Mayo. Is Balla located in Crossboyne. Patrick's father's name was Terence. His last name does appear to be uncommon in Ireland.
The name Martin was not duplicated with my New Orleans family. Only Terence, Thomas, Rosetta, Hugh, Michael and James seemed to be used in his immediate family.
I did locate him in the 1851 English census living with a Bryan and Thomas Ansborough in Bradford England. It was a big breakthrough because he lived very close to his future bride Ellen Fitzpatrick. I did locate their marriage document and the birth of their first son Thomas. I do not know the relationship of the Bryan and Thomas. The name Bryan was never used in New Orleans.