§ 6-122. Designation or nomination; eligibility, restrictions. A person shall not be designated or nominated for a public office or party position who (1) is not a citizen of the state of New York; (2) is ineligible to be elected to such office or position; or (3) who, if elected will not at the time of commencement of the term of such office or position, meet the constitutional or statutory qualifications thereof or, with respect to judicial office, who will not meet such qualifications within thirty days of the commencement of the term of such office.