After the filing of a nomination petition by or in behalf of a proposed candidate for a city office, such candidate shall not be permitted to withdraw unless a written notice of withdrawal is served on the city clerk not later than 4:00 o'clock, eastern standard time, in the afternoon of the third day after the last day for filing petitions as in this Charter provided, unless the third day falls on a Saturday, Sunday or legal holiday, in which case the notice of withdrawal may be served on the clerk up to 4:00 p.m. o'clock, eastern standard time, on the next secular day.