Any taxpayer may appeal from the allowance of any claim against a city of the first class, except a tort claim as defined in section 13-903, by serving a written notice upon the city clerk within ten days from such allowance and giving bond as provided in section 16-727. When the city council, by ordinance, provides for the publication of the list of the claims allowed, giving the amounts allowed and the names of the persons to whom allowed, in a legal newspaper in or of general circulation in such city, such appeal may be taken by a taxpayer by serving a notice thereof within such time after such publication as may be fixed by such ordinance, and giving bond for such appeal within ten days after such allowance.