After the Great Fire of Rome in 64 AD, we don’t hear anything definite about the Christians for forty years. There’s nothing that’s for sure about Christians until the reign of the Roman Emperor Trajan, about 100 AD.
Suetonius does not use the word Christian. But to a Roman maybe the Christians seemed to not believe in the gods. (After all, Christians didn’t believe in the Roman gods.) And then in 96 AD, some people at court conspired to kill Domitian. One of the main people involved in the assassination was a man named Stephen. And Stephen is a Christian name. Was that a plot by Christians, or partly by Christians?
The main thing we can gather from this information is that apparently Christianity itself was not yet illegal at this time. But nobody really knows whether Domitian ever killed people for being Christians or not. And nobody knows whether it was Christians who killed Domitian, either.