Every person having a claim or demand against a county shall file with the clerk of the county court thereof an account or statement of the same, fully setting forth the items; and where the claim or demand is for services for which no rate or compensation is fixed by law or by such court, the number of days occupied in such services. The clerk shall present such account or statement to such court at its first meeting thereafter, which shall allow the whole or such part thereof as it may deem just, or disallow the whole.