Flavius Josephus (c. 37 CE – c. 100 CE) was a first-century Jewish historian who chronicled the destruction of First Jewish–Roman War (66–73 CE) in two works: The Jewish War (c 75 CE) and Antiquities of the Jews (c 94 CE).
The Testimonium Flavian, a passage from Josephus' Antiquities of the Jews, is often cited by apologists as independent, 1st century confirmation of the existence of Jesus. However, there are many problems with the passage including it breaking the flow of the chapter that it appears in and no one noting it until the 4th century.
Even if the paragraph was entirely genuine based on Carrier's examples of Ned Ludd and John Frum it would still not show Jesus existed as a human being simply because it is too brief. Nevermind that there is no consensus on exactly what parts of the Testimonium Flavianum (if any) are actually from Josephus.
This is a passage that also tends to get used as evidence of Jesus. It doesn't have the same problems the Testimonium Flavian has but there are still issues with it.
With the exception of Jerome every other reference (Hegesippus, Clement of Alexandria, Eusebius of Caesarea, and Early Christian tradition) the death of James the Just is put around 69 CE by being thrown from a battlement, stoned, and finally clubbed to death by passing laundrymen. The James in Josephus was killed in 62 CE by just stoning.
Moreover Rufinus of Aquileia in the 4th century stated James the Lord's brother was informed of the death of Peter (64 CE or 67 CE ie after the James in Josephus was dead and gone).
Origen is often used to prove that this passage is not an interpretation but both of his supposed references claim that Josephus made direct connection between the death of James and the fall of the Temple:
"this writer" (Josephus)… "in seeking after the cause of the fall of Jerusalem and the destruction of the temple"… "says nevertheless"… "that these disasters happened to the Jews as a punishment for the death of James the Just, who was a brother of Jesus (called Christ)". - Against Celsus 1.47
"But at that time there were no armies around Jerusalem, encompassing and enclosing and besieging it; for the siege began in the reign of Nero, and lasted till the government of Vespasian, whose son Titus destroyed Jerusalem, on account, as Josephus says, of James the Just, the brother of Jesus who was called Christ, but in reality, as the truth makes dear, on account of Jesus Christ the Son of God." - Against Celsus 2.13
The "Jamesian Reference" has no connection between the death of its James and the fall of the Temple.
Furthermore Christ was a title not a name and Josephus gives examples of many would be Christs that caused trouble:
Simon of Peraea (d 4 BCE).
Judas, son of Hezekiah (4 BCE).
Matthias, son of Margalothus (during the time of Herod the Great) - thought by some to be the "Theudas" referenced in Acts 5.
Athronges (c 3 CE).
Judas of Galilee (6 CE).
The Samaritan prophet (36 CE) killed by Pontius Pilate.
Theudas the magician (between 44 and 46 CE).
Egyptian Jew Messiah (between 52 and 58 CE). Supposedly led an army of 30,000 people in an attempt to take Jerusalem by force which the Romans drove back, killing 400 and capturing 200. According to Josephus he "came out of Egypt to Jerusalem" and "He advised the crowd to go along with him to the Mount of Olives, as it was called, which lay over against the city, and at the distance of a kilometer."
An anonymous prophet (59 CE)
Menahem, the son of Judas the Galilean (66 CE)
Jesus ben Ananias [Ananus] (66-70 CE). Suggested by Carrier as being the raw template for the Passover section of "Mark"
Menahem ben Judah (sometime between 66-73 CE).
John of Giscala (d c70 CE)
Simon bar Giora (69-70 CE)
Jonathan, the weaver (73 CE)