Eugene is a graduate of Fort Hill High School and Allegany Community College, where he earned an AA degree in Business Administration. While in college, he was employed in the summer months by Pittsburgh Plate Glass (PPG) and Allegany Ballistics Laboratory (ABL). Eugene also worked at the Kelly Springfield Tire Company, the Western Maryland Consortium, and at CSX Transportation, where he retired from on November 2, 2015 after 33 years of employment.
Councilman Frazier was elected in November of 2016 to the Cumberland City Council to serve a 4-year term, was re-elected November 2020, and was sworn into office on January 7, 2021. Eugene currently serves on the Human Relations Commission.
Eugene resides in Cumberland with Felicia Taylor. Between them they have 5 children and 6 grandchildren.