Superstitiously is the adverb: it describes doing something in a way that is driven by superstition. It attaches to an action — 'she superstitiously touched the wood', 'he superstitiously refused to say the number out loud', 'they superstitiously kept the old coin in the till'. What it adds is a small explanation of why the person did the thing: not for a real reason, but because of a belief about luck. It is a fairly bookish word. In speech people usually say it a longer way — 'because he's superstitious', 'out of superstition' — while the single adverb turns up more in novels and articles, often placed right before the verb, where it lets the writer explain a character's odd little action in one word without stopping the sentence.