"He does not wear a coat."
Translation:Hij draagt geen jas.
Those last two would sound extremely awkward to the ears of a native speaker. See here: https://www.duolingo.com/comment/3734833 . Basically, if you could phrase the English sentence using "no" + noun (in this case: "he wears no coat"), then the Dutch translation would use "geen" instead of "niet".
Well, if you literally translate what you have written there it would not make sense in English, either. You would not say "he wears no a jacket", you would simply say "he wears no jacket" (which although is not the best way to express this in English; it is the best way to express the sentence in Dutch as discussed above).