N.Y. Real Prop. Acts. Law § 389

§ 389. Any person interested may appear and defend. Any person\ninterested in the property, or whose interests may be affected by the\nfinal order or judgment of registration in the proceeding, whether\nspecifically named in the notice or not, may enter his appearance by\nserving a copy of the same on the registrar of the county in which the\nproperty is located and with the clerk of the supreme court in such\ncounty, and filing the original thereof together with proof of service\nwith the county clerk on or before the return day or within such further\ntime as may be allowed by the court; and may enter his objections, if\nany, by likewise serving a copy of the same on the registrar of the\ncounty in which the property is located and with the clerk of the\nsupreme court in such county, and filing the original thereof together\nwith proof of service with the county clerk on or before the return day\nor within such further time as may be allowed by the court; and may\noppose the petition for registration of the property as belonging to the\npetitioner, or set up a cross-demand to have the title registered in his\nown behalf. In any case, he shall state particularly what his interest\nis and shall specifically state all objections to the petition.\n