Yes there were Harrisons of Ballybay. However, your Letitia Mitchell married first a John Harrison (born about 1801, d. 1841) whose father was James Harrison [Jr.] of Church Hill, County Monaghan and who immigrated to Smithville, Chenango County New York. James Jr. married Elizabeth Kinnier. All of JOhn's siblings went and stayed in the U.S., some in New York City, some in Smithville.
The Ballybay Harrisons and the Church Hill Harrisons were by 1760 second cousins. They both go back to a Mr. Harrison who arrived in County Monaghan in about 1700. His Harrisons were from the area around Ballynahinch, County Down. (See Ballynahinch Presbyterian records for Harrison baptisms starting in 1703. These are on the Ros Davies website for County Down.)