St Paul is the author of Hebrews, the council of Trent says so and so do many of the Early Church Fathers, people say the theology is clearly Pauline, but the reason they suspect it is not St Paul is because of the language and style is somewhat more elegant. St Jerome explained that St Paul had wrote Hebrews in Aramaic and had it translated into Greek, according to Eusebius this translator was St Luke, who was more elegant in his writing, and so Hebrews resemble’s St Luke’s work of Acts of the Apostles.
for more evidence St Paul is the original writer:
“Many of the believing Jews in Palestine had been deprived of all their goods, and scattered over the world, as he [St Paul] mentions in the Epistle to the Hebrews”—St John Chrysostom, Commentary on Galatians 2:10
“He wrote nine epistles to seven churches: To the Romans one, To the Corinthians two, To the Galatians one, To the Ephesians one, To the Philippians one, To the Colossians one, To the Thessalonians two; and besides these to his disciples, To Timothy two, To Titus one, To Philemon one. [13 total so far] **The epistle which is called the Epistle to the Hebrews is not considered his, on account of its difference from the others in style and language, but it is reckoned, either according to Tertullian to be the work of Barnabas, or according to others, to be by Luke the Evangelist or Clement afterwards bishop of the church at Rome, who, they say, arranged and adorned the ideas of Paul in his own language, though to be sure, since Paul was writing to Hebrews and was in disrepute among them he may have omitted his name from the salutation on this account. He being a Hebrew wrote Hebrew, that is his own tongue and most fluently while the things which were eloquently written in Hebrew [ie Aramaic] were more eloquently turned into Greek **and this is the reason why it seems to differ from other epistles of Paul….Gaius, bishop of Rome, in the time of Zephyrinus, that is, in the reign of Antoninus, the son of Severus, delivered a very notable disputation Against Proculus, the follower of Montanus, convicting him of temerity in his defence of the new prophecy, and in the same volume also enumerating only thirteen epistles of Paul, says that the fourteenth, which is now called, To the Hebrews, is not by him, and is not considered among the Romans to the present day as being by the apostle Paul.”—St Jerome On Illustrious Men Chapters 15 & 59
“The apostle Paul writes to seven churches (for the eighth epistle—that to the Hebrews—is not generally counted in with the others).”—St Jerome, Letter 53
“Paul’s fourteen epistles are well known and undisputed. It is not indeed right to overlook the fact that some have rejected the Epistle to the Hebrews, saying that it is disputed by the church of Rome, on the ground that it was not written by Paul. But what has been said concerning this epistle by those who lived before our time I shall quote in the proper place.”—Eusebius, Church History Book III Chapter 2
“Thus Ignatius has done in the epistles which we have mentioned, and Clement in his epistle which is accepted by all, and which he wrote in the name of the church of Rome to the church of Corinth. In this epistle he gives many thoughts drawn from the Epistle to the Hebrews, and also quotes verbally some of its expressions, thus showing most plainly that it is not a recent production…. For as Paul had written to the Hebrews in his native tongue, some say that the evangelist Luke, others that this Clement himself, translated the epistle.”—Eusebius, Church History Book III Chapter 38
“He [Clement of Alexandria] says that the Epistle to the Hebrews is the work of Paul, and that it was written to the Hebrews in the Hebrew language; but that Luke translated it carefully and published it for the Greeks, and hence the same style of expression is found in this epistle and in the Acts.”—Eusebius, Church History Book VI Chapter 13
“In addition he [Origen] makes the following statements in regard to the Epistle to the Hebrews in his Homilies upon it: "That the verbal style of the epistle entitled ‘To the Hebrews,’ is not rude like the language of the apostle, who acknowledged himself ‘rude in speech’ [2 Corinthians 11:6] that is, in expression; but that its diction is purer Greek, anyone who has the power to discern differences of phraseology will acknowledge.”—Eusebius Church History Chapter 26 on Origen
“As Luke also may be recognized by the style, both to have composed the Acts of the Apostles, and to have translated Paul’s Epistle to the Hebrews.”—Fragments of St Clement of Alexandria Chapter 1 last line
“And he says that the Epistle to the Hebrews is Paul’s, and was written to the Hebrews in the Hebrew language; but that Luke, having carefully translated it, gave it to the Greeks, and hence the same coloring in the expression is discoverable in this Epistle and the Acts; and that the name" Paul an Apostle" was very properly not prefixed, for, he says, that writing to the Hebrews, who were prejudiced against him and suspected, he with great wisdom did not repel them in the beginning by putting down his name….And now, as the blessed Presbyter used to say, since the Lord, as the Apostle of the Almighty, was sent to the Hebrews, Paul, as having been sent to the Gentiles, did not subscribe himself apostle of the Hebrews, out of modesty and reverence for the Lord, and because, being the herald and apostle of the Gentiles, his writing to the Hebrews was something over and above [his assigned function.]”—Eusebius on Clement of Alexandria, Ecclesiastical History, VI. 14.
[Eusebius aware of the arguments for and against Hebrew’ source states]: “such as are contained in the Epistle to the Hebrews, and in many others of Paul’s Epistles.”—Eusebius Church History Book II, Chapter 17 on Philo