The process of imprinting coins under authority has changed a lot since the Roman Empire. The video linked here shows the mechanical processes used to mint a modern American quarter. One part of the video to pay special attention to: even after the quarter is officially stamped and looks and feels like a quarter, it does not yet have value until the issuing authority sends it out of the facility. In other words, the authority assigns it the value: https://www.youtube.com/watch?v=HRpRz2P4l2g.
Hebrews1:3 declares that Jesus is “the exact imprint of [God’s] nature.” The term is used only here in the New Testament, and it has a lot of background in coin making. It is also used on a coin minted by Kotys II, a king of Thrace. Based on analysis of the use of the term, “The attestation of [karaktēr] on the coinage of Kotys II is not primarily related to the image on the coin but rather to the authority to strike/mint the coin, it is after all, an image of Herakles not Kotys on the coin. It would therefore be appropriate to translate Hebrews 1:3a, given the context of the passage and the background of the term, as: ‘He is the radiance of God’s glory and the authenticating mark of God’s very being, and he sustains all things by his powerful word’” (Michael P. Theophilos, “The Numismatic Background of [Karaktēr] in Hebrews 1:3,” Australian Biblical Review 64 : 78–79).