E or ę, and a or ą is based on the noun case. The word by itself ends in a (ryba) but if it is the object of the verb, it ends in ę (rybę). At least that is what Duolingo says is true in this case. Duolingo doesn't explicitly teach this idea, you have to go elswhere. Search for 'noun case' and 'declension'.
I think the confusion comes out as "ta" gets declined as "tę" while "tamta" as "tamtą". 99% of feminine adjectives are declined (in accusative form) as "-ą", while feminine nouns as "-ę". "Tę" (being an adjective) can therefore considered as an exception (I hope moderators will confirm what I'm saying). Powodzenia!
You get check the conjugation of verbs on Wiktionary:
If it was a 'type what you hear' exercises, those currently don't show you that you had a typo.
On our side, I see that "Jesz tamto rybę" should have been rejected. But sometimes the grading may be different on a different platform (PC/Android/iOS), they all have separate systems.