does a minnesota conciliation court have jurisdiction in new jersey?

Since I do not know what a conciliation court is, I cannot answer your question.  If it is a state court, its jurisdiction is limited to whatever enabling laws created it, and in any event, it is constrained by the geographic limitations of the jurisdiction which created.  In other words, it probably does not have jurisdiction in New Jersey.  That said, I don't know the purpose for you asking the question, and there are means and methods for taking judgments from other states and getting those judgments entered in New Jersey.