Before any claim against a city of the metropolitan class, except officers’ salaries earned within twelve months or interest on the public debt is allowed, the claimant or the claimant’s agent or attorney shall verify such claim by affidavit, stating that the several items mentioned in such affidavit are just and true and the services charged or articles furnished, as the case may be, were rendered or furnished as charged in such affidavit, and that the amount charged and claimed in such affidavit is due and unpaid, allowing all just credits. The city comptroller and the comptroller’s deputy shall have authority to administer oaths and affirmations in all matters required by this section. All claims against the city must be filed with the city clerk. When the claim of any person against the city is disallowed, in whole or in part, by the city council, such person may appeal from the decision of such city council to the district court of the same county, as provided in section 14-813.