§ 3. Members of common council; appointments to other city offices. No member of the common council of any city shall, during the period for which he was elected, be capable of holding under the appointment or election of the common council any office the emoluments of which are paid from the city treasury, or paid by fees or compensation directed to be paid by any act or ordinance of the common council, but this section shall not affect the right to any fees or emoluments belonging to any office, provided, however, that in any city having a city manager or council-manager form of government in which a mayor and vice-mayor may be elected or appointed from the membership of its council, such mayor and vice-mayor may, in addition to the emoluments received as councilman, receive compensation for their services from the city treasury as mayor and vice-mayor. An officer of any city who violates any provision of this section shall be guilty of a misdemeanor and on conviction thereof his office shall be vacant.