In an excellent article, scholar and prolific blogger, R. Joseph Hoffmann summarised the evidence for the historicity of Jesus that can be got from Paul's letters.
Professor Hoffmann shows that people who think they can find members of Jesus's family in Paul's letters or in Josephus are simply misguided.
Professor Hoffmann wrote
It is sometimes pointed out that Paul makes reference (Galatians 4.4) to Jesus having “been born of a woman, under the law,” but it is widely believed that these words are an insertion into the text of Galatians: Marcion, our earliest witness, does not know them, and as Hilgenfeld once noted, if his opponent, Tertullian, could have quoted them against Marcion, a docetist thinker, to prove the essential humanity of Jesus, he would have. We are left with the bare fact that Paul knows nothing of the human family of Jesus.
Professor Hoffmann continued :-
It is known by scholars, however, that Christian references in Josephus’s work are pious additions. In the case of the Jamesian reference, the hand of the Christian editor is especially badly disguised by the addition of “who is called Christ” following the use of the name “Jesus” in discussing the trial of a certain James.
It is an echo of the same device used in the Testimonium Flavianum (Antiquities 18.3), sometimes cited as a proof of the existence of Jesus but today normally regarded as a Christian forgery. If we purge the Christian interpolation, it is clear that the James mentioned by Josephus, who is delivered to stoning, is the brother of a significant Jewish leader and contender for the priesthood, Jesus bar Damneus, whose name appears in the same passage.
In Antiquities 20.9.4, a Jesus bar Gamaliel succeeds Jesus the son of Damneus in the high priesthood. Josephus does not mention – at all – the James known from New Testament sources. The James sentenced to stoning is a completely different man.
Professor Hoffmann continues :-
The basis for the suggestion that James is the brother of Jesus depends on early references in Paul, especially Galatians 1.19. There is no doubt that James was regarded by Paul as a significant player in the Jerusalem community, together with Peter and John (Galatians 2.9, repeated in the legendary primacy-catalogue of Mark 9.2ff.). But his use of the word adelphos, as many scholars recognize, refers to James as a member of the brotherhood, as in Galatians 2.4; 3.15; 4.12, or as when he speaks of “false brothers” in Gal 2.4,5. James, according to Luke, uses the same language in calling Paul “brother,” (Acts 21.20) and the community the “brotherhood” (20.17).