(1g)    In this section, “client responsible for payment” means a client of the state public defender other than a client entitled to legal representation without a determination of indigency.

   (3)   The board shall establish by rule a fee schedule that sets the amount that a client responsible for payment shall pay for the cost of the legal representation if the client does not pay the applicable discount fee under sub. (3m). The schedule shall establish a fee for a given type of case, and the fee for a given type of case shall be based on the average cost, as determined by the board, for representation for that type of case.

   (3m)   The board shall establish by rule a fee schedule that sets the discount amount that a client responsible for payment may pay during a time period established by rule instead of paying the applicable fee under sub. (3). The fee schedule shall establish a discount fee for each type of case included in the schedule under sub. (3). If a client responsible for payment pays the applicable discount fee within the time period established under this section, the client may not be held liable for any additional payment for counsel.

   (4)   The board shall establish by rule a fee schedule that sets the maximum amount that a parent subject to s. 48.275 (2) (b) or 938.275 (2) (b) shall pay as reimbursement for legal services and sets the maximum amount that a person subject to s. 51.605, 55.107, or 980.0305 shall pay as reimbursement for legal services. The maximum amounts under this subsection shall be based on the average cost, as determined by the board, for each applicable type of case.