”Jesus had come from a village in Judea, and was the son of a poor Jewess who gained her living by the work of her own hands. His mother had been turned out of doors by her husband, who was a carpenter by trade, on being convicted of adultery [with a soldier named Panthéra (i.32)]. Being thus driven away by her husband, and wandering about in disgrace, she gave birth to Jesus, a bastard. Jesus, on account of his poverty, was hired out to go to Egypt. While there he acquired certain (magical) powers which Egyptians pride themselves on possessing. He returned home highly elated at possessing these powers, and on the strength of them gave himself out to be a god.”

Celsus is claiming that the real father of Jesus is a Roman soldier named Pantera. Initially, my thoughts were ‘how could Celsus have known this a hundred years later for a fact?’ He was notoriously anti-Christian and could merely have made these statements in an attempt to embarrass the fledgling religion.

The Bingerbrück Tombstone
A tombstone was found in 1859 in Bingerbrück, Germany with the following inscription:

“Tiberius Julius Abdes Pantera from Sidon, aged 62 years served 40 years, former standard bearer(?) of the first cohort of archers lies here”.

Additional Sources
This story is also found in the Tosefta (Jewish oral law from the period of the Misnah), the Qohelet Rabbah (an Aggadic commentary of Ecclesiastes) and the Jerusalem Talmud (Rabbinic notes on the second century Jewish oral tradition). In the Tosefta, Chullin 2:22-24, there are two mentions of a man named Jacob who names his mentor as being Yeshu ben Pandera (Jesus, son of Panthera) where a miracle of healing is performed in his name.

So, did Jesus’ mother have an illicit affair with a Roman soldier named Panthera and fall pregnant by him? I don’t know.
But to be honest these specifics are beside the point. What is more likely, that Mary had a sexual relationship with someone other than Joseph or that she was impregnated by god?