In any supplemental proceeding, where it appears to the court that a judgment debtor may have an interest in or title to any real property, and such interest or title is disclaimed by the judgment debtor or disputed by another person, or it appears that the judgment debtor may own or have a right of possession to any personal property, and such ownership or right of possession is substantially disputed by another person, the court may, if the person or persons claiming adversely be a party to the proceeding, adjudicate the respective interests of the parties in such real or personal property, and may determine such property to be wholly or in part the property of the judgment debtor. If the person claiming adversely to the judgment debtor be not a party to the proceeding, the court shall by show cause order or otherwise cause such person to be brought in and made a party thereto, and shall set such proceeding for hearing on the first open date in the trial calendar. Any person so made a party, or any party to the original proceeding, may have such issue determined by a jury upon demand therefor and payment of a jury fee as in other civil actions: PROVIDED, That such person would be entitled to a jury trial if the matter was adjudicated in a separate action.