(4) If the mother or father so objects or if the tutor so appointed as aforesaid considers that the mother or father is unfit to have the custody of the minor, the tutor may apply to the Court, and the Court may either refuse to make any order (in which case the mother or father shall remain sole tutor) or make an order that the tutor so appointed shall act jointly with the mother or father, or that he shall be sole tutor of the minor and in the latter case may make such order regarding the custody of the minor and the right of access thereto of its mother or father as, having regard to the welfare of the minor, the Court may think fit, and may further order that the mother or father shall pay to the tutor towards the maintenance and education of the minor such weekly or other periodical sum as, having regard to the means of the mother or father, the Court may consider reasonable.