It is hereby made the duty of the sheriffs of the several counties of this state to serve and execute all process directed to them by said judges of probate in their respective counties, and shall be subject to fine and amercement as provided by law for the neglect or refusal to discharge the duties required of them; and it is hereby made the duty of the sheriff of each county, or his deputy, to attend the probate court of his county, under the direction of the judge thereof.