No sum paid into the court as provided in § 24-12-12 shall be charged with clerk’s fees of any nature. After the filing of the copy, plat, and statement, notice of the taking of the land, or interest therein, shall be served upon the owners of and persons having an estate in and interested in the land by a member of the division of sheriffs, leaving a true and attested copy of the description and statement with each of the persons personally, or at their last and usual place of abode in this state with some person living there, and in case any of the persons are absent from this state and have no last and usual place of abode therein occupied by any person, the copy shall be left with the persons, if any, in charge of or having possession of the land, or interest therein, taken of the absent persons if the same are known to the officer; and after the filing of the resolution, plat and statement, the secretary of the authority shall cause a copy of the resolution and statement to be published in some newspaper published in the county where the land, or interest therein, may be located, at least once a week for three (3) successive weeks. If any person shall agree with the authority for the price of the land, or interest therein, so taken, the court upon the application of the parties in interest, may order that the sum agreed upon be paid immediately from the money deposited, as the just compensation to be awarded in the proceeding.