Separately is the correct spelling the other is not a word, it is a misspelling.

To Gillian's perfect answer, I will add: "Separate" is a famous English "spelling demon." It is one of the words that native English speakers have trouble learning to spell correctly. It is often misspelled. One reason is that the adjective and adverb forms are pronounced almost like "sep-rit" or "sep-rit-ly." Neither of the "a's" is given the usual pronunciation--they are almost left out. If you didn't know the spelling, you'd NEVER guess it was spelled with two "a's."