Do we have good evidence that Paul or any of the original twelve Apostles died for their belief in the risen Jesus? Nope. Nevertheless, Justin Bass claimed so in a lecture you can view online (Evidence of the Apostles’ Martyrdom).
But first I want to post my observations of that previous lecture he gave that pertains to the subject. I viewed and annotated that in preparation for our debate, and had all my notes ready at the table. And yet, though Bass leaned on this claim in our debate (the famous “No One Would Die for a Lie” gambit), I didn’t need to get into much detail to refute his argument against the clock.
As I noted in the debate, he couldn’t establish that they died for anything more than a vision, and visions are ubiquitous across religions—even now, but then especially. He couldn’t even establish that they could have avoided their deaths by recanting. Or even that what they died for was their belief in the resurrection, rather than their moral vision for society, or (I could have added) some other belief they wouldn’t recant—such as their already-Jewish refusal to worship pagan gods, the only thing Pliny really ever killed Christians for (the resurrection was never even at issue); and that’s the only explicitly eyewitness account we have of any Christians being killed for anything in the whole first hundred years of the religion.
But there is a lot more to be said.