Paul claims that he was shown mercy so that “Jesus might demonstrate His perfect patience as an example (hupotyposis) for those who would believe in Him for eternal life” (1 Timothy 1:16). Paul is “typical,” a pattern or impress, for others who find mercy.
How exactly? The earlier verses tell us: He was a blasphemer and a persecutor and a violent aggressor against Jesus and His church (1:13). He acted ignorantly in unbelief, but the favor of Jesus was more abundant (1:14).
He is ignorant like his Jewish bothers, who didn’t grasp the import of the prophets that are read every Sabbath, which spoke of Christ Jesus (Acts 13:27).
Jesus forgave his sin of ignorance, and showed mercy, and so Paul became a type not for sinners in general, but specifically for first-century Jews who were also persecutors, blasphemers, and violent aggressors against Jesus.
This is why Paul calls attention to himself in his argument concerning Israel’s conversion in Romans 9-11. He is not simply saying, “I’m a saved Jew; therefore, God still intends to save Jews.” He is saying, “I was an enemy of Jesus, and Jesus turned me; He will also turn my brothers who are enemies of Jesus.”
Paul is typical not only in being a converted sinner; he is typical in being a Jewish opponent of Jesus turned by Jesus.