Lewis & Short

Midaium, i, n., = Μιδάειον, a city of Phrygia, Plin. 5, 32, 41, § 145.
Hence, subst.: Midaeenses, ium, m., the inhabitants of Midaium, Cic. Fam. 3, 8, 3.
Also called Midaei, orum, m., Plin. 5, 29, 29, § 105.