This family were lived in the territory of Fearnmuigh or Fearnmaigh [which means 'the territory of the plain'] is an area in South Monaghan/South Armagh and is in fact the present Barony of Farney, whose principal town is Carrickmacross.
Ó Tighearnaigh of Uí Fiachrach Muaidhe
This family were Lords of Carra. Almost the only family member recorded in the annals was Flann Ó Tighearnaigh.Gilbert Ó Tigernaig, Bishop of Annaghdown, 1306-1323 was also a member of this family.
Ó Tighearnaigh of Brega
This family claimed descent from Tigernach mac Fócartai (died 865), one of the Kings of Brega. They were a branch of the southern Uí Néill. The Kingdom is said to have stretched from Birr in Co. Offaly to the Hill of Uishneach in Westmeath. Tighearnach resided at the Great Crannóg of Lagore, which is situated near Ratoath in County Meath, not far from Dublin. Tighearnach led the Irish to a great victory over the Norse in 848 A.D.
Ó Tighearnaigh of Ormond
A family of the name resided in Ormond, nowadays County Tipperary. Their origins are obscure . New research now confirms that this family was indeed an indigenous sept. Their seat was in the townland of Park and their lands, Fearann Ó Tighearnaigh, took in most of the present-day townlands of Ballymackey, Ballyknockane, Carrowea, Clash, Falleen, Gortnadrumman, Kilgorteen and Knockane.
Ó Tighearnaigh of Corcu Modruad
This is an area in northern Clare. This sept were hereditary Priests and Monks.
Brian Tierney (born 1957), American businessman and newspaper publisher