The third canon of the Second Ecumenical Council (Constantinople, 381)

Τὸν μέντοι Κωνσταντινουπόλεως ἐπίσκοπον ἔχειν τὰ πρεσβεῖα τῆς τιμῆς μετὰ τὸν τῆς Ῥώμης ἐπίσκοπον, διὰ τὸ εἶναι αὐτὴν νέαν Ῥώμην.

Hefele, C.J., Histoire des conciles d'après les documents originaux II.1, trn. in french. Leclercq, D.H. (Paris 1907), p. 24.

The legend on the transfer of the palladium of Rome to Constantinople by Constantine I and the name of the Tyche of Constantinople:

καὶ ἔστησεν ἐν μέσῳ κίονα πορφυροῦν μέγαν λίθου Θηβαίου ἀξιοθαύμαστον, καὶ ὑπεράνω τοῦ αὐτοῦ κίονος ἔστησεν ἑαυτοῦ ἀνδριάντα μέγαν, ἔχοντα ἐν τῇ κεφαλῇ αὐτοῦ ἀκτίνας, ὅπερ χαλκούργημα ἤγαγεν ἀπὸ τῆς Φρυγίας. ὁ δὲ αὐτὸς βασιλεὺς Κωνσταντῖνος ἀφελὼν κρυπτῶς ἀπὸ Ῥώμης τὸ λεγόμενον Παλλάδιον ἔθηκεν αὐτὸ ἐν τῷ ὑπ' αὐτοῦ κτισθέντι φόρῳ ἀποκάτω τοῦ κίονος τῆς στήλης αὐτοῦ, ὥς τινες λέγουσι τῶν Βυζαντίων ἐκ διαδοχῆς ἀκούσαντες. τὴν δὲ τύχην τῆς πόλεως τῆς ὑπ' αὐτοῦ ἀνανεωθείσης ποιήσας θυσίαν ἀναίμακτον ἐκάλεσεν Ἀνθοῦσαν.

Chronicon paschale, ed. L. Dindorf, vol. Ι (CSHB, Bonn 1832), p. 528.

The founding of Constantinople according to the Chronicle of Constantine Manasses (mid-12th c.)

[...] τὴν πανευδαίμονα πόλιν τῶν Βυζαντίων,
καὶ πόλιν ὀλβιόπολιν αὐτῇ προσανεγείρει,
Πόλιν τὴν μεγαλόπολιν, πόλιν τὴν νέαν Ῥώμην,
Ῥώμην ἀεὶ νεάζουσαν, ἀεὶ καινιζομένην,
Ῥώμην ἀφ' ἧς προσχέονται χαρίτων αἱ συρμάδες

Migne, J.P. (ed.), Patrologia Graeca 127, col. 308.

Constantinopolitan aristocracy as descendants of the Roman senatorial class

[...] τοὺς ἀξιολόγους τῶν εὐπατριδῶν καὶ τιμίων ἐν ταύτῃ τῇ νέᾳ Ῥώμῃ μεθ' ἑαυτοῦ παραλαβὼν [ο Κωνσταντίνος] μετῴκισέ τε καὶ συμπολίτας ἑαυτοῦ ἀπειργάσατο, λαμπρὰς οἰκίας τούτοις ἐπιδειμάμενος κατὰ τὴν ἐμφέρειαν τῶν ἐν τῇ παλαιᾷ Ῥώμῃ πολυτελῶς κατεσκευασμένων οἴκων. ἐκ τούτων οὖν, ὡς ὁ λόγος αἱρεῖ καὶ ἡ τοῦ γένους ἀναφορὰ περιάγει, οἱ Φωκάδες αὐτοὶ καταγόμενοι τήν τε περιφάνειαν ἄνωθεν ἔσχον καὶ τὸ τῆς ἀνδρίας ἀλκιμώτατον καὶ ανύποιστον, ἐκ τῶν ὀνομαστῶν ἐκείνων Φαβίων, ὥς που διὰ βίβλου τινὸς παλαιᾶς ἐχειραγωγήθην ποτέ, τὴν ἀρχὴν τοῦ γένους ἐφέλκοντες.

Bekker, I. (ed.), Michael Attaliotae, Historia (Corpus Scriptorum Historiae Byzantinae, Bonn 1853), p. 218.

A representation of the Tyche of Constantinople in a 6th-C. mosaic designated as Rome:

The currency of the name Rome as a straightforward designation of Constantinople is nowhere more stikingly displayed than in the great mosaic at Madaba, Jordan, from the Room of Hippolytus that was excavated beneath the Church of the Virgin. A later 6th floor displays a scene of the Graces and Erotes in the upper register of an elaborate mosaic, with the myth of Hippolytus in the lower register. In the upper border sit three personifications, or tychai, of cities. They are identified as Rome, Gregoria and Madaba. Each has a headpiece. Rome's is a kind of Phrygian cap, whereas Gregoria and Madaba wear turreted crowns typical of city tychai. Under the misapprehension that Rome here was the Italian city, scholars have struggled without success to find some way to recognise Constantinople in Gregoria. Since Madaba is dearly present as the site of the mosaic, it had been assumed that the other two cities were presumably great ones - obviously Rome and the mysterious Gregoria. But there is no way that Constantinople could have been called Gregoria, and there is no need to look for such a name. Rome in this mosaic is Constantinople. Her headpiece matches precisely the one worn by the image of Constantinople in the Peutinger Table. As for Gregoria [...] Antioch nicely fills the bill. It was a city that we know tried to rid itself of its Seleukid name in the 6th C., when it enjoyed the stewardship of the eminent Bishop Gregorius.

Bowersock, G., «Old and New Rome in the Late Antique Near East», στο P. Rousseau - M. Papoutsakis (ed.), Transformations of Late Antiquity. Essays for Peter Brown (Ashgate 2009), p. 47.