The only difference between the two is usage. "Not ever" is often more emphatic. "I asked my friend if he eats peanut butter and he said, 'not ever'." "Never" could also be used here, but "not ever" puts more emphasis on the answer. "My friend told me he never eats peanut butter." My friend told me he does not ever eat peanut butter." The second sentence empasizes the fact.

Moorche is incorrect. Both cases mean he does not go there.

Do you go there?.........not ever.........goes sometimes. Do you go there?..........never.........does not go there.