New Testament: Are there authenticated texts by the authors of the canonical New Testament books (like the Evangelists or Paul) but which are excluded from the canon?

##Summary The closest you'll get to this is the Secret Gospel of Mark, and that one is highly controversial.

All that we have of this Secret Gospel of Mark are three bits of text discovered in 1958 (or thereabouts) by Morton Smith, a professor at Columbia University. Smith found these quotes in a letter which attributed them to the same author who wrote the canonical Gospel of Mark.

This Secret Gospel of Mark appears to use the same vocabulary and grammatical style that the canonical Mark does. However, the actual pages discovered by Morton Smith have since been lost. All we have are his pictures and descriptions.

To make matters even worse, some experts are of the opinion that the vocabulary used by the author of the Secret Gospel is too much like Mark. As if someone is intentionally emulating Mark's writing style! As far as I can tell there is no broad consensus, but a majority of experts seem to think that Morton Smith forged the whole thing.

##Full Story Dozens of non-canonical early Christian texts exist, but most of them either lack attribution or are claimed to be written by someone other than the canonical writers of the New Testament. For example the Gospel of Mary or the Gospel of Judas. There are some texts that are claimed to have been written by the same author as one or more of the canonical biblical texts. An example is the Gospel of Peter, which claims to be written by the apostle Peter to whom the canonical Petrine epistles are attributed. Very few, if any, experts would give this claim any credence however. In fact, even the two Petrine epistles are generally considered to have been written by two different authors neither of whom was the biblical Peter.

Methods

How do we know such claims to be false? We do not have the original manuscripts so we can not carbon date them, or the ink used to write them. What we have is copies of copies of copies (and so on). Therefore experts need to look for clues in the text. They analyze the vocabulary and writing style of each document. From this type of analysis they can draw a number of conclusions with varying degrees of certainty. For example whether two texts were written by the same author (high certainty, particularly with longer texts) or during which time period or in which location the text was written (low certainty if going by vocabulary alone, much higher if there are specific clues in the text).

These methods have led to centuries of debate regarding the canonical Pauline epistles in particular. When the non-canonical early Christian texts started to be rediscovered in large numbers they were eagerly analysed in the same fashion! Most of these texts can plausibly be dated to a period later than any of the canonical gospels or letters. To get back to your question: are any of these texts written by the same author as one of the canonical texts? Only one text can somewhat plausibly make this claim, and that is the mysterious Secret Gospel of Mark.

Discovery of the Secret Gospel

Morton Smith visited Jerusalem in 1941, when he was still a student. Due to the Second World War he found himself unable to return home to the United States. Therefore he went to stay at the Mar Saba monastery, where he found a large collection of interesting manuscripts in complete disarray. In 1958 Morton Smith, now a professor at Columbia University, decided to take a sabbatical and return to the monastery to try and organize its library.

What Morton Smith discovers then is a little bit complicated, so I'll format it as a list:

Smith discovers a book published in 1646...
...with empty pages in the back, upon which a text is written in typical 18th century handwriting...
...this text turns out to be a copy of a hitherto unknown letter by church father Clement of Alexandria...
...in which Clement discusses and repeatedly quotes a hitherto unknown Secret Gospel of Mark, said to be written by the same Mark who wrote the canonical gospel

Smith realized the importance of his discovery and went to work on it, eventually publishing two books about Clement's letter and the quotes purported to be from Mark.

Is it a Forgery?

Smith's discovery was controversial from the moment he published it. The quotes attributed to Mark depict Jesus engaging in a mysterious ritual, spending the night with a barely clothed young man who appears to be in love with Jesus. (You can find a link to the full text below.) You can see why this is controversial, even apart from the question of authenticity!

Points in favour of authenticity:

The handwriting is typical for the 18th century
The vocabulary and writing style in Clement's letter are similar to the vocabulary and writing style of the known letters by Clement
The vocabulary and writing style in the quotes of the Secret Gospel are similar to the vocabulary and writing style of the canonical Mark
The monks of the monastery say that they have seen the pages before their disappearance, and appear to believe it genuine

Points in favour of it being a forgery:

Only one small group of experts have seen the actual book, other than Morton Smith. The book has been lost since 1977. Therefore, the pages nor the ink have ever been carbon dated. (Finding a 17th century book with empty pages wouldn't be much of a feat, but finding usable ink from back then is virtually impossible.) All we have now are pictures
A plausible argument can be made that the text by Clement is a little bit too typical of Clement
And similarly Mark's text is a bit too typical of Mark, using words he uses a lot even more often than he does in the canonical gospel
Morton Smith dedicated one of his books about The Secret Gospel to "the one who knows". Who is this person and what does he or she know...?

##Sources

Morton Smith wrote two books about his discovery. The Secret Gospel (1973) is intended for the lay audience. His other work, Clement of Alexandria and a Secret Gospel of Mark (1973) is more technical.
Bart Ehrman's 2003 book Lost Scriptures: Books that Did Not Make It into the New Testament has a chapter on the Secret Gospel of Mark and contains the full text thereof. It's also an interesting read for anyone who wants to learn more on this subject.
Full text of the Secret Gospel of Mark