The board shall make and keep a roster of all persons eligible and available for appointment to each class of positions in the service of the city, ranked according to ability, except that no examination shall be given and no roster kept for positions to be filled by persons designated by the board as common laborers. Layoffs available for reemployment shall be placed at the head of the proper present and subsequent eligible rosters in the inverse order of their terminations. Employees who voluntarily terminate their services may be granted reemployment status under proper eligible rosters under the circumstances and in the manner as may be provided for in the rules and regulations of the board, subject to stipulations of this section concerning layoffs. Persons desiring appointment may file applications with the board, and the board, from time to time, shall conduct examinations to test the ability of the applicants. All qualified applicants shall be examined, and examinations shall be public, competitive, and, subject to limitations specified by the board as to any factors pertinent to the ability of an applicant to discharge the duties of the position, shall be open to all persons legally authorized to work in the United States and the State of Alabama. Examinations shall be practical in character and shall relate to those matters which test the ability of the person examined to discharge intelligently the duties of the position for which he or she applies. The board may charge each applicant a reasonable examination fee to be determined by the board. In no case shall an appointment be made from an eligible roster which is more than two years old, and no eligible roster shall be the result of more than one type of examination.