The Supreme Court exercises original jurisdiction in cases

Disputes between two or more states, disputes between a state and the federal government, disagreements between two cities

The most frequent exercise of the Supreme Court's original jurisdiction has been in cases between two or more states.

Explanation:

I'm not sure what your question is, but the Supreme Court has original jurisdiction (a case is tried before the Court) over certain cases, e. g., suits between two or more states and/or cases involving ambassadors and other public ministers.