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My answer will be based on the assumption that OP is talking about when 「なんか」 is indeed followed, not preceded, by a noun as s/he so states in the comments (but not in the question). In informal conversation, there actually exists such a structure. "なんか + Noun + みたいな（のような） + Noun" For instance, I have little appetite when I have a fever. Since I do ...
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