Answer:

The answer is that there is no evidence that Apollos wrote the book.  Really, all there is is speculation about this.  No one knows who wrote Hebrews.  Some have proposed Paul, but most reject this hypothesis because it does not appear to be written in his style. Others have proposed Barnabas because he was Jewish and a respected leader.  Still others have speculated that Apollos and even Aquila wrote the book.  All these guesses are really just guesses because the early church did not record who wrote the book.  I like the word of Origen, the most influential Christian theologian and Christian author in the third century.  His opinion on the authorship of Hebrew was “Only God knows who wrote the book of Hebrews.”  I suppose the guess that Apollos wrote the book is about as good as any other theory, but it is really speculation.

John Oakes