My family is from a small town in Syria that was the hometown of Phillip the Arab, and was named Philippopolis under his rule (it is now called Shabah). The city is filled with Roman ruins, including a small ampitheatre. Whenever I visited it, I noticed a small fish carved into the stone on one of the walls. From what I could tell, it was very old and not modern graffiti (which the rest of the structure was completely free from). Did the fish symbolize anything to the romans of the time, either for cultural or practical purposes (i.e. maybe it meant something to those who built the ampitheatre)?
EDIT: 3 things... Firstly, I made a grammar mistake in the title :( (*significance OF). Secondly, it may have been a raised engraving (popping out from the stone) instead of being carved in. I cant remember exactly as I have not been back in a few years for obvious reasons. Finally, the fish was very small, only about 2 or 3 inches long.
The fish, or ichthys, was a symbol used by early Christians to identify themselves. If it was on a building, it was likely that that was the home of a Christian or a place of worship, or both as the two often overlapped, especially in the earliest days.
EDIT: Rereading your post, you say it was on an amphitheater. Someone else may have to explain that relationship.