(a) For the purposes of this Code section, the term "conviction" means a final judgment of conviction entered upon a verdict of guilty or upon a plea of guilty. Such judgment shall be deemed to be a final judgment when the remittitur from the appellate court of this state affirming the conviction is filed in the court below or, if the proceeding is before a federal court, when the United States Circuit Court of Appeals has affirmed the conviction.

(b) The Governor and any county or municipal governing authority shall, in their discretion, offer and cause to be paid rewards for the detection or apprehension of the perpetrator of any felony committed within this state, such reward not to exceed the sum of $1,000.00 in felonies not capital, including arson, and not to exceed the sum of $10,000.00 in capital felonies and arson; provided, however, that the governing authority of a county or municipality may offer and pay such a reward only in cases in which the Governor has first offered a reward and, in such cases, the amount offered by any local governing authority shall not exceed $25,000.00.

(c) The Governor shall, at the Governor's discretion, offer and cause to be paid rewards for the detection or apprehension of cattle, horse, ratites, or swine thieves stealing cattle, horses, ratites, or swine within this state; and such reward shall not exceed $1,000.00.

(d) The Governor, at his discretion, may pay any reward authorized by this Code section after conviction.

(e) No reward provided for in this Code section shall be paid to any officer who arrests such person in the regular discharge of his duty by virtue of process in his hands to be executed, nor to any person who has arrested the offender prior to the publication of the reward.