presidial

adj

1. Belonging to a province, or being like a province; provincial.
2. Pertaining to a president or one who presides; presidential.

   “the doorway was vacant save for a large brindled cur that stood upon the threshold, wagging his tail and watching the scene with a suave, indulgent, presidial gaze, as if he were the patron of the ball.”

3. Having or relating to a garrison.

   “There are three presidial castles in this city.”