People always wonder are there any coins specifically associated with the holiday of Purim (the book of Esther) such as perhaps coins bearing the portrait of the Persian King Achashveirosh (Aheusauros - Xerxes) or Mordechai.
While we do not have a direct portrait coin, coins struck by the Persian empire during that period certainly do exist. The most common archaic Persian coin is the Persian Siglos. A gold coin of the same size and similar design, but heavier, is called the Daric. The daric is mentioned in the Bible as the coin "Darkemon."
The Persian Siglos was minted in Lydia a province of Persian, while the governmental seat of the vast Persian empire was in the east. For the most part these Lydian, Persian coins did not circulate in a significant way in the east or in Shushan the capital of Persia (in spite of the claims of some entrepreneurial coin dealers), though they did circulate in the Western Persian Empire. Trade in Shushan for the most part would have taken place with precious metals or through barter. Still the Lydian, Persian coins paid homage to the great King at Shushan, and the Siglos, which was struck (in slightly varying varieties) over a period of 200 years did bear an image of a Persian King going forth in battle. The king though, is generic in form, and does not depict any specific ruler. All the coin designs were similar but they did change somewhat as time went on. Thus the initial issue is thought to depict/represent Darius I while later issues would represent Xerxes (Achashveirosh) and other later kings.
In a sense, even without the royal portrait, these coins were ahead of their time, in that they depicted the king altogether. For the most part, in the early stage of coinage (7th - 5th centuries) only dieties and national symbols were featured on coins. Conversely, although the incuse punch was a feature of early coinage that was largely abandoned by the 4th Century, the Siglos was consistently minted until its final days with the simple reverse of an incuse punch. Thus, while virtually all cultures were already striking sophisticated two sided coins, the Lydians persistently stuck to the one sided coins of the "Great King".
As far as depictions of other officials: There were actually many coins struck within the Persian empire, mainly Cilicia, that did strike coins of secondary rulers, usually satraps (even Judaea did!) But, it is difficult to pinpoint who a particular non-godlike figure on a coin was meant to be, and the issues we do know of (i.e. Mazaios, Balakros etc.), do not point to Mordechai. So while it is possible that some coin depicts the Viceroy Mordechai, it is impossible to say so with certainty.
Nevertheless, for those building a growing coin collection, the coins of Persia, Caria, Cilicia.... provide an intriguing series of coinage for collecting and study and are tied to the Bible as well.