May I suggest taking it to one of the maritime museums such as the McLarty Treasure Museum, located at 13180 North A1A, just south of Sebastian Inlet State Park. Have a curator look at your piece & get an opinion. At first glance, the piece looks to be Chinese export pottery, 17th-18th century, However, the edges seem a bit sharp for the pieces having been tumbled in the shifting sands for hundreds of years.
Decades ago, I found a small bag full of export porcelain (Asian) shards along Governor's Beach, Grand Turk island, in 1987. The beach & shallow waters were abundant with them. All pieces showed wear to the edges, from being tossed in the surf & sand, with the edges being rounded & smoothed over rather than angular. Not saying that yours is more modern, but, I'd get an expert's opinion. It's a neat find, & you should be back combing that area.
(attached a pic from my 1987 trim to Grand Turk ... "my" cannon ...