Except as otherwise provided for, no special election shall be held, and no ordinance, in which any petition or protest is required, shall be referred to, or voted on, at any election unless, within the time allowed by the terms hereof, a sufficient petition or petitions, addressed to the mayor, demanding such election or protesting against or requesting the adoption of such ordinances, shall be personally signed by at least twenty-five per centum of all the qualified electors of such city and filed with the city clerk. Immediately upon the filing of any such petition or petitions with the city clerk, he shall endorse thereon the date of such filing and shall within ten days thereafter, verify the signatures thereto by the registration and poll books, and deliver such petition or petitions to the mayor of such city, together with the certificate of such clerk showing the total number of qualified electors of such city and also the total number of qualified electors who shall have signed such petition or petitions, which certificate shall be prima facie correct but not conclusive. If it shall appear from said petition or petitions and the certificate of such clerk that the same are in proper form and have been signed by the required number of the qualified electors of such city, it shall be the duty of the council at its next regular meeting to order such special election, or refer such ordinance to a vote of the electors of such city, in case of their failure to wholly repeal the same. Each and every petition shall, at the time the same is filed with the city clerk, have attached thereto the affidavit of one or more of the signers thereto, stating the total number of names signed to such petition at the time of filing the same, and no such petition shall be received or filed by the city clerk unless such affidavit is attached thereto.