Accepted as canonical.
Author accepts, others dispute.
Some time ago I made a rough copy of a chart that I had come across which shows the development the canon underwent in formation. I'm glad I sketched it out, as it comes in handy in this discussion now. :)
So I made a quick color-coded gif to post here. The chart actually extends to the right some, to include books like The Shepperd of Hermas, The Apocalypse of Peter, The Wisdom of Solomon, among others, which were generally accepted as genuine and authoritative by the early commentators, but I kept it to these twenty-seven books for the sake of brevity here.
I did a bit of searching and found sufficient citation to support my argument from the previous post's comments.
I have emphasized the relevant bits in the following citations:.
According to [Metzger, Bruce M. The Canon of the New Testament: Its Origin, Development, and Significance. Clarendon Press. Oxford. 1987.] p. 159:
In another treatise Tertullian cites a passage from the Epistle to the Hebrews (6:4-8), which he attributes to Barnabas as the author, 'a man sufficiently accredited by God, as being one whom Paul had stationed next to himself'. (De pudic. 20)
Throughout Origen's writings he quotes from the Epistle to the Hebrews more than 200 times, and in the vast majority of his references he is content to attribute it to Paul as its author. But near the close of his life (after 245 CE), where Origen is speaking as a scholar, he admits that the tradition of its authorship is wholly uncertain. From the composite account in [ Eusebius. The History of the Church (Ecclesiastical History)]:
In addition he makes the following statements concerning the Epistle to the Hebrews, in his Homilies upon it: 'That the character of the diction of the Epistles entitled 'To the Hebrews' has not the apostle's rudeness in speech, who acknowledged himself to be rude in speech (2 Cor. 6:6), that is, in style, but that the Epistle is better Greek in the framing of its diction, will be admitted by everyone who is able to discern differences of style. But again, on the other hand, that the thoughts of the Epistle are admirable, and not inferior to the acknowledged writings of the apostle, this also everyone who carefully examines the apostolic text will admit'. Further on he adds, If I gave my opinion, I should say that the thoughts are those of the apostle, but the style and composition belong to some one who remembered the apostle's teachings and wrote down at his leisure what had been said by his teacher. Therefore, if any church holds that this Epistle is by Paul, let it be commended for this also. For it is not without reason that the men of old time have handed it down as Paul's. But who wrote the Epistle in truth, God knows. Yet the account that has reached us [is twofold] , some saying that Clement, bishop of Rome, wrote the Epistle, and others, that it was Luke, the one who wrote the Gospel and the Acts. (6.25.11-14)
I find it curious that someone would express shock at my positing Marcion as evidence that Hebrews is not Paul's work, I think it is quite adequate and sufficient evidence—think about it, Marcion the collector and freak of all things Pauline, probably the man who inspired the "church" to establish a canon more than anyone else (the move toward establishing a canon was arguably a direct response to Marcion, in fact) has never heard of the epistle to the Hebrews. Why my suggestion (i.e. that Marcion's omission speaks against Pauline authorship) would elicit a "Wow!" is beyond me. Being that the epistle does reflect some aspects of pauline thought, there's no reason to think that Marcion knew of it but rejected it. Likewise for the Muratorian canon. Nowhere is this epistle mentioned there. So . . . why has Marcion never mentioned this text. The answer clearly is that he has never heard of it (though there IS reason to think that it predates Marcion, which only means that it wasn't attributed to Paul until right before Irenaeus's day—though even HE disputed its authenticity). This deserves more than a glossing over and dismissing it out of hand. I would welcome any alternate explanations for the silence in both Marcion and the Muratonian fragment regarding Hebrews and also for the controversy reflected in the texts regarding its authorship, where even as late as the time of Eusebius the matter is not yet either settled or even a necessary belief. Notice that this argument against Pauline authorship of Hebrews is completely independent of any analysis of the Greek subjunctives. When multiple independent trajectories of research all come to a conclusion (a kind of interdisciplinary planetary alignment) the very fact of these independently-arrived-at agreements reinforces that conclusion.