25:19a

They only had some contentions with him: The phrase some contentions refers to topics that Paul and the Jews disagreed about. Other ways to translate this clause are:

All they had were some arguments (Good News Translation)
-or-
they had certain points of disagreement (New Revised Standard Version)
-or-
they argued with him (Contemporary English Version)

their own religion: The Greek word that the Berean Standard Bible translates as religion can also mean “superstition.” The word “superstition” mocks those beliefs as wrong. But Festus probably intended the meaning that did not mock the Jewish religion, because Agrippa had an official connection to the Jewish religion. The Greek word often refers to beliefs that are different from the beliefs that the speaker holds. Paul used a similar Greek word in 17:22b (“very religious”). Other ways to translate this word are:

the beliefs that they hold
-or-
the things they themselves believe
-or-
what they themselves believe about their God

25:19b

a certain Jesus who had died, but whom Paul affirmed to be alive: Festus knew that Jesus had died, but also heard Paul talk about God resurrecting Jesus. The Romans, in their own religion, did not believe in resurrection. Other ways to translate this are:

about a man named Jesus, who has died; but Paul claims that he is alive (Good News Translation)
-or-
a certain Jesus, who had died, but whom Paul asserted to be alive (New Revised Standard Version)
-or-
about a man named Jesus who died. But Paul said that he is still alive (New Century Version)

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