Instructions
Study your coin and make notes. Take note of how exactly milled it is, including if it's completely round or roughly round; the details of the face on the coin; which direction the face is looking; what the text on both sides of the coin is and even the metal it's made from. Take pictures of the coin from a variety of angles.
Compare your coin to historical examples found in museums or online. Links in the Resources section have images of Gordian III coins, both heads and tails sides. Compare every detail, from the text to the metal to the shape to the face, and see how well your coin measures up against genuine articles.
Contact experts. If you remain unsure about your coin's authenticity, go to coin collectors who specialize in Roman coins, history professors and experts on the period, or even musems to find out how genuine your coin is. If you can't tell based on your own visual inspection, then it never hurts to ask for aid from knowledgeable sources.