Bruce, Vicky is absolutely right: a picture (preferably a photo) is essential before we can attempt an interpretation. Time passes, however, and the inscription becomes more and more intriguing, prompting such idle speculation as the following:
The inscription actually reads GROMPHISOU NIKA (apologies for the Greeklish; the converter wouldn't help here), "Winner of the javelin-throw" (lit. "He is winner at the javelin-throw"). "Gromphos" is a type of javelin mentioned in Hellenistic authors (Polybius, Strabo). "Gromphisis" (by analogy with "akontisis") refers to a contest of javelin-throwing. We are bothered by the genitive ending -OU rather than the correct -EOS, but such mixed inflection may have passed in Byzantine times. Those of you in Greece who have access to proper source materials may have more to say about that. The same goes for my groundless assumption that such a sports victory could be commemorated by a ring in the (early?) Byzantine period. Here on the flooded, storm-blasted Oregon coast, access to a good research library is out of the question.
Of course, the above interpretation could be torpedoed instantly by a photo of the ring and its inscriptionespecially if the ring turns out to be sized for a woman's (or child's) finger! So please post the picture at your earliest convenience. Expectantly, Bill