Heb, authorship
    "As distinctive among the writings of the NT as Hebrews is, we
    actually know very little about its origin, its author, and its first readers.
    The traditional and ancient designation of the book as 'The Epistle of Paul the
    Apostle to the Hebrews', found, for example, at the head of the book in the KJV,
    is not a part of the original document, but is rather an opinion of the early
    church that first comes to expression in the Eastern church (Alexandria) late in
    the second century and in the Western church two centuries after that. Moreover,
    this ascription appears to have been inferred from the document itself, much in
    the manner of modern scholarship, rather than derived from any independent
    tradition about its origin. The result is that we are left to draw such
    conclusions as we can from the actual contents of Hebrews" (NIBC).
    
    "The epistle was used by Clement of Rome and probably also by
    Polycarp and Hermas. Therefore the author was an early Christian. The earliest
    reference to authorship is a statement of Clement of Alexandria that Paul wrote
    it in Hebrew and that Luke translated the work into Greek (quoted in Eusebius,
    Eccl Hist 6:14:2). When it was accepted as part of the NT, this was partly at
    least because contemporaries held Paul to be the author. This view, however,
    appears to rest on no reliable evidence but rather to be a deduction from the
    facts that Paul was a prolific writer of epistles and that Hebrews is a noble
    writing that must have had a distinguished author. But both the language and
    thought forms are unlike those of Paul. The Greek is polished; Paul's is rugged,
    though vigorous. This book moves in the context of Levitical symbolism, about
    which Paul elsewhere says nothing. The same argument also tells against Clement
    of Alexandria's view that Luke translated it. While there are some interesting
    coincidences of language between Hebrews and Luke-Acts, there are also some
    differences. And it is incredible that if Luke knew Hebrews, he should have made
    no reference whatever to its teaching either in his Gospel or in the Acts. [The
    mention of Timothy, in Heb 13:23, also suggests Paul's authorship.]
    
    "None of the early writers who cites the epistle mentions its
    author. Nor does internal evidence help us much. The author was plainly a
    teacher, a second generation Christian (Heb 2:3). The style is unlike that of
    any other NT document; consequently, we have nothing more to go on to determine
    authorship than conjecture. Though many suggestions have been made, it will
    suffice to mention only a few of them. The allegation that Barnabas was the
    author is as old as Tertullian, but little can be said in its support. Barnabas
    was a Levite (Acts 4:36), and there is much about Levitical ritual in the
    epistle. Again, in Acts 4:36 Barnabas was called 'huios parakleseos' ('son of
    encouragement'); and in Heb 13:22 the epistle refers to itself as 'my word of
    exhortation' [or 'encouragement': the sw]. But it is hard to see Heb 2:3 as
    applying to Barnabas. 
    
    "Luther suggested that Apollos was the author. A number of
    modern scholars support this view. Apollos was an eloquent man (Acts 18:24), and
    there is indeed eloquence in this epistle. Apollos came from Alexandria, a
    center where allegorical interpretation, which might be said to be akin to the
    method used in Hebrews, flourished. Apollos had 'a thorough knowledge of the
    Scriptures' (Acts 18:24), a description particularly appropriate for the author,
    who did not simply use the 'proof-text' method but applied a thorough knowledge
    of Scripture in an original manner. Apollos must remain a possible author, but
    the evidence is far from conclusive. 
    
    "Harnack thought that Priscilla probably wrote the epistle.
    His strong point is that this would account for the suppression of the author's
    name. It was a man's world, and there would be every reason for keeping it quiet
    that a woman had written an epistle intended to be authoritative and to have
    wide circulation. Priscilla and her husband were cultured Hellenistic Jews, and
    the woman who could instruct Apollos in the faith (Acts 18:26) was no mean
    teacher. The interest in the tabernacle would be natural in a family whose
    living came from tentmaking (Acts 18:3), and the outlook of a pilgrim would be
    natural to one who did so much traveling. All this is interesting but plainly it
    falls far short of proof. And against it stands the masculine participle
    'diegoumenon' ('to tell') used of the author in Heb 11:32. 
    
    "In the end we must agree that we have no certain evidence
    about the authorship of Hebrews. Who wrote it remains unknown to us. We can
    scarcely improve on the words of Origen's conclusion, that 'who wrote the
    Epistle, God only knows the truth' (Eusebius, Eccl Hist 6:25:14)"
    (EBC).