The superior courts have authority:

(1) To exercise original, exclusive, or concurrent jurisdiction, as the case may be, of all causes, both civil and criminal, granted to them by the Constitution and laws;

(2) To exercise the powers of a court of equity;

(3) To exercise appellate jurisdiction from judgments of the probate or magistrate courts as provided by law;

(4) To exercise a general supervision over all inferior tribunals and to review and correct, in the manner prescribed by law, the judgments of:

(A) Magistrates;

(B) Municipal courts or councils;

(C) Any inferior judicature;

(D) Any person exercising judicial powers; and

(E) Judges of the probate courts, except in cases touching the probate of wills and the granting of letters of administration, in which a jury must be impaneled;

(5) To punish contempt by fines not exceeding $500.00 and by imprisonment not exceeding 20 days; and

(6) To exercise such other powers, not contrary to the Constitution, as are or may be given to such courts by law.