What they had against him were certain disputes about their own religion, and about a dead man called Jesus who Paul insisted was alive.
In context
17So they came here with me, and without any delay I took my seat on the tribunal the next day and ordered the man brought in. 18When his accusers stood up, they brought no charge of the crimes I had been expecting. 19What they had against him were certain disputes about their own religion, and about a dead man called Jesus who Paul insisted was alive. 20Being at a loss how to investigate such matters, I asked whether he was willing to go to Jerusalem and be tried there on these charges. 21But Paul appealed to be kept in custody for the decision of the Emperor, so I ordered him held until I could send him to Caesar.”