Suetonius is one of three key Roman authors who may refer to early Christians, the other two being Pliny the Younger and Tacitus. These authors refer to events which take place during the reign of various Roman emperors, Suetonius writing about the Claudius expulsion and Nero's persecutions, Tacitus referring to Nero's actions around the time of the Great Fire of Rome in 64 AD, while Pliny's letters are to Trajan about the trials he was holding for Christians around 111 AD. But the temporal order for the documents begins with Pliny writing around 111 AD, then Tacitus around 115/116 AD and then Suetonius around 122 AD.
The Roman historian and senator Tacitus referred to Christ, his execution by Pontius Pilate and the existence of early Christians in Rome in his final work, Annals (written ca. AD 116), book 15, chapter 44.
"Consequently, to get rid of the report, Nero fastened the guilt and
inflicted the most exquisite tortures on a class hated for their
abominations, called Christians by the populace. Christus, from whom
the name had its origin, suffered the extreme penalty during the reign
of Tiberius at the hands of one of our procurators, Pontius Pilatus,
and a most mischievous superstition, thus checked for the moment,
again broke out not only in Judæa, the first source of the evil, but
even in Rome, where all things hideous and shameful from every part of
the world find their centre and become popular. Accordingly, an arrest
was first made of all who pleaded guilty; then, upon their
information, an immense multitude was convicted, not so much of the
crime of firing the city, as of hatred against mankind".
Pliny the Younger, the Roman governor of Bithynia-Pontus (now in modern Turkey) wrote a letter to Emperor Trajan around 112 AD and asked for counsel on dealing with Christians. The letter (Epistulae X.96) details an account of how Pliny conducted trials of suspected Christians who appeared before him as a result of anonymous accusations and asks for the Emperor's guidance on how they should be treated.
The Roman historian Suetonius (c. AD 69 – c. AD 122) makes reference to early Christians and possible reference to their founder in his work Lives of the Twelve Caesars.
Roman Emperor Claudius reigned 41 to 54 AD. Suetonius reports his dealings with the eastern Roman Empire, that is, with Greece and Macedonia, and with the Lycians, Rhodians, and Trojans.
In Claudius 25 Suetonius refers to the expulsion of Jews by Claudius and states (in Edwards' translation):1
"Since the Jews constantly made disturbances at the instigation of Chrestus, he expelled them from Rome."