Fellowship applicants compete only against other applicants from the states of their legal residence. 

As funding permits, the Foundation plans to offer one fellowship per state per year.

https://www.jamesmadison.gov/https://www.jamesmadison.gov/questions.php

What is a "qualifying master's degree program"?

The fellowships are intended exclusively for graduate study leading to a master's degree. James Madison Fellows may attend any accredited institution of higher education in the United States. Each individual entering the James Madison Fellowship Program will be expected to pursue and complete a master's degree in one of the following (listed in order of the Foundation's preference):

• Master of Arts (MA) in American history, political science, or government
• Master of Arts in Teaching (MAT) concentrating on either American Constitutional history (in a history department) or American government, political institutions, or political theory (in a political science department). MAT degrees without required constitutional coursework cannot be approved.
• Master of Education (MEd) or the Master of Arts or Master of Science in Education with a concentration in American history or American government, political institutions, and political theory