N.Y. Comp. Codes R. & Regs. tit. 22 § 600.19
If, subsequent to the filing of a notice of appeal, the sole issue sought to be reviewed is the amount of compensation awarded to a judicial appointee (i.e., referee, arbitrator, guardian, guardian ad litem, conservator, committee of the person or a committee of the property of an incompetent or patient, receiver, person designated to perform services for a receiver, such as but not limited to an agent, accountant, attorney, auctioneer or appraiser, person designated to accept service), the appeal may be prosecuted in accordance with any of the methods specified in section 600.5 of this Part; or in lieu thereof may be prosecuted by motion in accordance with the procedure applicable to special proceedings, section 600.2(b) of this Part. In such event, the review may be had on the original record, and briefs may be filed at the option of the parties.
N.Y. Comp. Codes R. & Regs. Tit. 22 § 600.19