On the one hand, there is the uneqivocable "ἐγὼ Παῦλος", used 6 times in his epistles, and the other hand there is the inferential style of ὁ μαθητὴς ὃν ἐφίλει ὁ Ἰησοῦς, used by the Evangelist when speaking of himself.
Relevent verses are:
2Corinthians 10:1 (Authours: Paul and Timothy) wrote:Αὐτὸς δὲ ἐγὼ Παῦλος παρακαλῶ ὑμᾶς διὰ τῆς πρᾳότητος καὶ ἐπιεικείας τοῦ χριστοῦ, ὃς κατὰ πρόσωπον μὲν ταπεινὸς ἐν ὑμῖν, ἀπὼν δὲ θαρρῶ εἰς ὑμᾶς·
Galatians 5:2 (Authour: Paul) wrote:Ἴδε, ἐγὼ Παῦλος λέγω ὑμῖν, ὅτι ἐὰν περιτέμνησθε, χριστὸς ὑμᾶς οὐδὲν ὠφελήσει.
Ephesians 3:1 (Authour: Paul) wrote:Τούτου χάριν ἐγὼ Παῦλος ὁ δέσμιος τοῦ χριστοῦ Ἰησοῦ ὑπὲρ ὑμῶν τῶν ἐθνῶν,
Colossians 1:23 (Authours: Paul and Timothy) wrote:[τὸ εὐαγγέλιον] οὗ ἠκούσατε, τοῦ κηρυχθέντος ἐν πάσῃ τῇ κτίσει κτίσει τῇ ὑπὸ τὸν οὐρανόν, οὗ ἐγενόμην ἐγὼ Παῦλος διάκονος.
1 Thessalonians 2:18 (Authours: Paul, Silas and Timothy) wrote:διὸ ἠθελήσαμεν ἐλθεῖν πρὸς ὑμᾶς, ἐγὼ μὲν Παῦλος καὶ ἅπαξ καὶ δίς, καὶ ἐνέκοψεν ἡμᾶς ὁ Σατανᾶς.
Philemon 19 (Authours Paul and Silas) wrote:ἐγὼ Παῦλος ἔγραψα τῇ ἐμῇ χειρί, ἐγὼ ἀποτίσω· ἵνα μὴ λέγω σοι ὅτι καὶ σεαυτόν μοι προσοφείλεις.
John 13:23 wrote:Ἦν δὲ ἀνακείμενος εἷς τῶν μαθητῶν αὐτοῦ ἐν τῷ κόλπῳ τοῦ Ἰησοῦ, ὃν ἠγάπα ὁ Ἰησοῦς·
John 19:26 wrote:Ἰησοῦς οὖν ἰδὼν τὴν μητέρα, καὶ τὸν μαθητὴν παρεστῶτα ὃν ἠγάπα , λέγει τῇ μητρὶ αὐτοῦ, Γύναι, ἰδοὺ ὁ υἱός σου.
John 20:2 wrote:Τρέχει οὖν καὶ ἔρχεται πρὸς Σίμωνα Πέτρον καὶ πρὸς τὸν ἄλλον μαθητὴν ὃν ἐφίλει ὁ Ἰησοῦς, καὶ λέγει αὐτοῖς, Ἦραν τὸν κύριον ἐκ τοῦ μνημείου, καὶ οὐκ οἴδαμεν ποῦ ἔθηκαν αὐτόν.
John 21:7 wrote:Λέγει οὖν ὁ μαθητὴς ἐκεῖνος ὃν ἠγάπα ὁ Ἰησοῦς τῷ Πέτρῳ, Ὁ κύριός ἐστιν.
John 21:20 wrote:Ἐπιστραφεὶς δὲ ὁ Πέτρος βλέπει τὸν μαθητὴν ὃν ἠγάπα ὁ Ἰησοῦς ἀκολουθοῦντα, ὃς καὶ ἀνέπεσεν ἐν τῷ δείπνῳ ἐπὶ τὸ στῆθος αὐτοῦ καὶ εἶπεν, Κύριε, τίς ἐστιν ὁ παραδιδούς σε;