Archaeologists have discovered Roman coins in the ruins of the 12th century Okinawa castle, Katsuren Castle. Analysis of the coins found them to bear the portrait of Constantine the Great, the Roman emperor from the early 4th century AD who mandated that Rome accept Christianity as the official religion. This is also the first discovery of Roman currency in Japan. Historically Okinawa has been associated with the Ryukyu Kingdom however the castle predates even that kingdom, going back to the local tribes and chieftains of an even earlier age. It was abandoned partly into a kingdom of Okinawa’s early history. Now these kingdoms were involved in trade with East and South East Asia (basically China to Indonesia) so it’s highly possible the coins arrived from India or China through trade further to the west with Muslims.
Rome would have been unable to have any trade with the island whatsoever. Triremes, the main kind of ship, couldn’t last outside the Mediterranean or if they got too far from the shore and Roman trade at its maximum extended to India, well short of even China itself. So the Okinawan ancestors wouldn’t be even close to Rome’s influence, meaning gradual trade or a traveling denizen of Rome has to be how they got there. It is important to remember that these coins remained in circulation for a while and were spread across the entire empire so a large amount were bound to wander the globe, finding their way into collections. Another issue is that coins from the Ottoman Empire were found dating to the late 17th century AD, well after the castle was abandoned. For this one? I have no clue that is quite a difficult puzzle. Personally I think the Roman coins just passed from person to person until it wound up in Okinawa, the same way we buy to build collections from objects found all over the world. But the mystery around it will surely foster future interest in discovering western artifacts across Asia.