On or before June 30, of each year, the county commission of every county shall, by order of record, designate all of the banking institutions, as defined in section two, article one, chapter thirty-one-a of this code, situated in the county and duly incorporated under the laws of any state, or organized under the laws of the United States, as depositories of public moneys: Provided, That in any county where no such banking institutions exist, or where such banking institutions fail, refuse or neglect to comply with all the provisions and conditions of this article, the county commission shall designate some qualified banking institution in some other county of this state convenient to the county seat. Risk and expense of making deposits in county depositories located outside of the county seat shall be borne by the banking institution in which the deposits are made. When any banking institution, designated by the county commission as provided by this section, has complied with all of the requirements and provisions of this article, the commission shall declare it a county depository.