Okay, I give up. I have most of the usual Byzantine coin books and the entire web at my disposal, but in four years and I have not found anything like this coin. It is an imitation of a Byzantine anonymous bronze, but with very usual "lettering" on the reverse. 28-27 mm. 7.58 grams. Base metal, less coppery than most Byzantine "anonymous bronze." The obverse could be Class A2 or Class E. The key difference is that class A2 has a four-line reverse legend and Class E has a three-line reverse legend. This one has three lines, but E is much scarcer than A2 so A2 is more likely to have been copied. Maybe it is just an approximation of A2 by someone who was not going to do the legend correctly anyway. With imagination I can see a few letters (at least "E", maybe "SILE") that might be part of "BASILE" in the middle line. I spent years thinking some of the letters looked like those on Armenian coins (which I can't read) and wondering if it could be an Armenian imitation. Then I wondered if the letters could be Georgian (from the Caucasus, not the one north of Florida). Has anyone seen anything published that is remotely like it? I am accepting advice about where to look next. If you have any odd Byzantine-like coins, feel free to post them.
That is very interesting! Lucky you for being able to hold it and study it in depth, @Valentinian! It really looks like a contemporary imitation. Maybe Armenian? For some reason the text almost seems like Armenian script. Maybe it's just gibberish? I think we can definitely rule out Roman government though.
You could check Georgian? Jesus Christ is in Georgian 4 - 6 letters (ieso krist’e, იესო ქრისტე). I see an "E" for sure at the end of the second line. I could be totally wrong but a suggestion.
I don't know how to do that. My OP mentioned that possibility, but I didn't know how then and I still don't know.
Valentinian. An intriguing query about that ancient coin depicted. Not easy to make out the details, though it does look like a halo around the figure. If a Christian coin, it could certainly be Byzantine, or perhaps Armenian etc. I think the only Byzantine Coin book I have is "Encounters - Travel and Money in the Byzantine World." By E. Georganteli & B. Cook. A small book, with lots of illustrations of Byz. Coins. One possible tactic - look up, on internet, Byzantine Coin Collection, The Barber Institute of Fine Arts, University of Birmingham. They have quite a vast collection of Byzantine coins, you could send pictures of your "odd" coin and ask if they have any ideas. I can't seem to find their leaflet, just now, but the internet should give contact details. Other than Byzantine, they also have Roman, Sasanian, Turkmen and Armenian coins. Do give it a try, it is one place where expertise exists !
Just a big stretch but you could take the text from the most similar byzantine coin and use google languages to translate it into the languages that you suspect. In this case Armenian and Georgian. Once you do that compare what you are shown with what you have. A previous poster gave you the Georgian for Jesus Christ. Suggest you look up the same in Armenian for comparison. good luck