The law permits cities to make their own laws. No preemption.
Syracuse may have its own rules, too. I don’t know.
If the permit clearly states which cities are exempt from the state permit, then yeah, it doesn’t apply in those cities. However, I have heard of some states slapping down such city ordinances in the same way they would say that a driver’s license for the state of California is valid in ALL areas of the state and, likewise, the traffic laws.
i.e. I don’t know that it would pass constitutional muster if it were ever challenged in court.