A fish, either dead or alive, is still "a fish" (one unit of a species of marine animal with scales, a set of fins, and which uses gills as a way to filter oxygen from its environment) before you start cooking it.
If you cook it whole it could still be "a fish" (fiŝo), but the general term for the food you get out of it is "fish" (fiŝajo).
"Fish is on the plate" is not a good phrase in English, in fact is sounds really "bad"! No one in English would come out and say a phrase like that, even with a plate of fish in his or her hand. I would rework this whole phrase in Esperanto so the translation ends up sounding like an English speaker would actually say it!!
It is acceptable to say "a (some) fish is on the plate." (followed by a look of either disgust or delight) In fact, I sometimes think that they forgot the a in the translation.
Redakto: after a year to think about it. This is foodstuff; fish as food, even in English, very rarely gets the indefinite article.
Mico12345 has part of it, but there's also the Yiddish (using non-Hebraic characters) Telar which, along with those he mentioned, comes from the middle high-German deller, which in turn is derived from the old French taillor, and, before that, from the Italian taglière (a table for cutting) and back into the Latin, a word which signifies a tailor.
Makes me want to make a costume made of dishes.
This has been repeated, but fiŝajo is a fish dish, a fish on the plate is just "fiŝo", dead or alive, not prepared to be eaten – unless you're some sort of cave man eating raw fish with skin on.
I have no problems with Esperanto but I get flagged all the time for my English (like "A fish dish is on the plate."), so this is more a test in English than in Esperanto for me.
If there were multiple fish, then sure, but when spoken about as food it's as bad as saying "food are on the plate."
This was answered already by Luis_Domingos:
"Fish are on the plate = Fiŝoj estas sur la telero (you only use the plural with the animal, not with the animal turned food - you don't say Food are on the table)."