I reached out to the producer and got the following response:
Thanks for forwarding the question.
In the Roman Empire there were strict laws for the wearing of rings by men, whether of iron or gold. Pliny the Elder discusses the subject in his Historia Naturalis, Book XXXIII, 29-33, noting that the iron ring had been distinctive of the equites (the class below the senators but above the regular citizens). Initially gold rings were reserved for senators, though some still held on to their traditional iron rings. The Emperor Septimius Severus (AD 193-211) extended the privilege of the iron ring to all soldiers, hence its importance in the Perpetua story (AD 203). As time went by, regulations became looser and privileges were extended to more and more people. (As a general rule, privileges are easy for governments to give and hard to take back.)
"Under the Empire the gold ring, although still regarded as a privilege and awarded as a military distinction, was very freely bestowed on all and sundry." Reynold Higgins, Greek and Roman Jewellery, Second Edition (London: Methuen & Co., 1980) 182
Higgins lists 14 kinds of rings. The one we show as worn by Cyprian is Type 2.
"2 A seal ring with a thick hoop, expanding slightly at the bezel… In the third century the ring becomes more elliptical in shape.”
This is the kind worn by Cyprian in the mid-third century. It should be worn on the fourth finger (the ring finger), but this ring was too big for the actor, so he wore it on the middle finger. The ring is deeply engraved with a classical figure so it can be used to seal documents. For a man of Cyprian’s status and wealth it would have been gold. We made this one in the studio and painted it gold. With a lot more time and money we could have had one made just for this actor, but that was a luxury beyond our reach.
Now we come to the pagan versus Christian aspect. Cyprian almost certainly wore such a ring as a pagan, not necessarily for religious reasons but simply the tradition of his family, and for authorizing documents. When he became bishop he would have needed such a ring for his official letters. Did he have a new ring made, or change the engraving in the one he had, or just continue to use what was on his hand? We don’t know.
Well, Customer 169638, sorry I don't know your name, but thanks for your interest and your keen eye for detail. We have tried more than most movies to be as historically accurate as possible. At times we slipped up. You will have noticed how the costumes change over the timespan of the series. Footwear, tunics, belts, helmets, swords, even the little clay lamps - it all changes. Sometimes we got it right spot on, sometimes approximately, and occasionally we messed up.