There is much extrapolation about the existence of a "President's book of secrets. " Only close insiders would know for certain. The movie, "National Treasure" raised this issue and, by blurring the line between fiction and reality, muddied the waters further.
Since the movie "National Treasure" there has been lots of talk about the book of presidents' secrets. It is an urban legend and does not really exist.
No, there is not a specific "President's Book of Secrets". There are, however, classified documents to which only a President, his staff, and cleared members of Congress can access.