He was, according to later medieval tradition, a rival of the High King, Conn of the Hundred Battles, and for a time after the year 123 was the de facto ruler of the southern half of Ireland.
Everything south of a line drawn between Galway Bay and Dublin was known as Leth Moga ("Mug's half") (Modern Irish: Leath Mhogha), and everything north of that line was Leth Cuinn ("Conn's half") (Modern Irish: Leath Chuinn).
His grandson Éogan Mór fought alongside Conn's son Art at the Battle of Maigh Mucruimhe, and is credited with founding the Eóganachta dynasty.
O'Rahilly speculated that Mug Nuadat may have been the god Nuada rather than an actual historical person.
Then he further goes on to say that this Eugene was commonly called "Mogha Nuadhad," and was a wise and politic prince and great warrior.