Fairfield is an small, rural, unincorporated village in northeastern Billings County, North Dakota, United States. It lies along U.S. Route 85, nort…Fairfield is an small, rural, unincorporated village in northeastern Billings County, North Dakota, United States. It lies along U.S. Route 85, northeast of the city of Medora, the county seat of Billings County. Its elevation is 2,756 feet. It has a cafe, an elementary school, and the post office serving the ZIP code of 58627.