Looks like early Delft ware, probably made in China. The Arms on it will have been drawn by an artist, with no knowledge of European heraldry, from a sketch or description provided by the family ordering the dishes / plates.
At a quick glance I can't see a likely family but I notice there is a fish over the castle. As a very long shot there is an Admiral Fish in the early 1800s who lived at Castle Fish in co. Kildare, Ireland in a village the Fish family had renamed after themselves. It is just possible that the Arms are a pun on the family residence. Or that may be pure coincidence !
Maec