According to MY gospel, God judges the secrets of men by Christ Jesus

[TonyChanYT]

Why did Paul say it was his gospel?

There were other man-made gospels floating around. Galatians 1:

8 But even if we or an angel from heaven should preach a gospel other than the one we preached to you, let them be under God’s curse!

To distinguish those, Paul wrote in Romans 2:

12 For all who have sinned without the law will also perish without the law, and all who have sinned under the law will be judged by the law. 13 For it is not the hearers of the law who are righteous before God, but the doers of the law who will be justified. 14 For when Gentiles, who do not have the law,

Paul addressed the Gentiles.

by nature do what the law requires, they are a law to themselves, even though they do not have the law. 15 They show that the work of the law is written on their hearts, while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them 16 on that day when, according to my gospel, God judges the secrets of men by Christ Jesus.

Paul's gospel focused on the Gentiles. He was not the author; Jesus was. He was the dispenser/ publisher/preacher of the gospel. According to Paul's gospel, Jesus judges the Jews and the Gentiles.

The Greek preposition is κατά. I think the English translation "according to" is a bit too strong and misleading. English Standard Version:

Remember Jesus Christ, risen from the dead, the offspring of David, as preached in my gospel,

Paul ended his letter NIV Romans 16:

25 Now to him who is able to establish you in accordance with my gospel, the message I proclaim about Jesus Christ, in keeping with the revelation of the mystery hidden for long ages past,

Paul received the gospel from Jesus.

26 but now revealed and made known through the prophetic writings by the command of the eternal God, so that all the Gentiles might come to the obedience that comes from faith— 27to the only wise God be glory forever through Jesus Christ! Amen.

Again, Paul emphasized the Gentile audiences for his gospel.

In what sense, it was Paul's gospel?

There were false gospels. There was also the gospel of the Twelve. Paul called it his gospel to distinguish his true gospel from Christ focusing on the Gentiles.