Illegibly is the adverb: you write, print, or sign in a way that other people cannot read. He signed his name illegibly means the signature is there, but it is only a scribble. The meaning you meant may be fine; the problem is the hand, the ink, or the mess on the page. Though actually, everyday speakers more often say so badly I cannot read it. Illegibly turns up when someone wants one tidy word for that idea, especially in writing about writing. Pair it with a verb of making marks: write, scrawl, sign, print. You do not say a person speaks illegibly — that would be about the voice, and this word is about what the eye can read.