Section 13 of Family Court Act

Section 13 of the Family Court Act, 1984 states that notwithstanding anything contained in any law, no party to a suit or proceeding before a Family Court shall be entitled, as of right, to be represented by a legal practitioner, provided that if the Family Court considers it necessary in the interest of justice, it may seek the assistance of a legal expert as amicus curiae.
It is important to note that in every court a legal practitioner has a right to appear on behalf of his client, the said right as per section 13 (as stated above) cannot be claimed before the family court, it is totally left to the discretion of the Family Court to allow any counsel on behalf of the client and give necessary legal assistance. So, if any of the parties before the Family Court filed a memo or petition seeking permission from the Court for him or her to engage a counsel and have legal assistance, the Family Court, may or may not allow the petition. When so allowed, the Counsel of a party could file the Vakalat and do all that is necessary for the client in the conduct of the case.
In your case, since you have already hired a lawyer and the court has allowed you to be represented by one, it is necessary for you to deposit the litigation fee.