Odo refers to the "Magistrate" a handful of a dozen times. But he's never shown, that I remember. So, who is he? Is he someone that is on the station, a character we know?
While I don't believe we've ever seen specifically who Odo is referring to, Deep Space Nine is technically owned by Bajor, and Starfleet is just administering it while they recover from the Occupation. So any magistrate that Odo is talking about is most like a Bajoran official. And we do know of at least one magistrate by name, Faren Kag. However, he was only magistrate of one village on Bajor - Odo would not have been talking about him for things happening on the station.
Most likely, Odo's usage of the word when talking to Jake and Nog is similar to mentioning a judge or jury to a youth here on Earth, hoping to guilt or worry them into admitting something.