The answer
James the brother of the Lord was James the son of Alphaeus and was at the same time Jesus' cousin according to the flesh, being the son of Jesus' maternal aunt who was Mary, the wife of Clopas. (Clopas was also named Alphaeus).
Children of one's maternal aunt were at that time regarded as one's brothers and sisters on the strength of this close tie of kinship according to the Jewish custom when one spoke of those born in the relationship.
For example, there is what the Bible says about the relationship of Jacob to his uncle Laban: "When Jacob saw Rachel the daughter of Laban his mother's brother, and the sheep of
Laban his mother's brother, that Jacob went near and rolled the stone from the well's mouth, and watered the flock of Laban his mother's brother. Then Jacob kissed Rachel, and lifted up his voice and wept. And Jacob told Rachel that he was her father's relative and that he was Rebekah's son. So she ran and told her father." (Gen. 29:10-12)
We see here that even though Laban was Jacob's uncle, Jacob was considered to be of Laban's 'own flesh and blood'.
We find that Laban also refers to Jacob as being one of his relatives when he invited him to look after his flocks: " Because you are my relative, should you therefore serve me for nothing? Tell me, what should your wages be. (Gen. 29:15)
The same thing happened regarding the relationship between Abraham and Lot.
Abraham was Lot's paternal uncle, and so the Bible said concerning the genealogy of the father of Abram and Haran (Lot's father) "Terah took his son Abram and his grandson Lot the son of Haran" (Gen.11:31). Nevertheless, when Lot left Sodom during the war against Kedorlaomer, the Bible says: " They also took Lot, Abram's brother's son who dwelt in Sodom, and his goods, and departed.... Now when Abram heard that his brother was taken captive, he armed his three hundred and eighteen trained servants who were born in his own house, and went in pursuit as far as Dan." (Gen 14:12-14)
So it was on account of these ancient customs that the sons of Christ's maternal aunt, Mary the wife of Clopas, were called Jesus' brothers and sons of Mary.
It was about this Mary, the wife of Clopas, that the Bible said: " Now there stood by the cross of Jesus His mother, and His mother's sister, Mary the wife of Clopas, and Mary Magdalene." (John 19:25). And this was the Mary mentioned by Mark when he said: " There were also women looking on from afar, among whom were Mary Magdalene, Mary the mother of James the Less and of Joses, and Salome,. " (Mark 15:40)
This James, Joses and Salome were all children of Mary the wife of Clopas, and it was they who were mentioned in what the Jews were saying about Christ: " Is this not the carpenter's son? Is not His mother called Mary? And His brothers James, Joses, Simon, and Judas?" (Matt. 13:55; Mark 6:3)
As for the Virgin Mary, she gave birth only to the Lord Christ, and then lived as a virgin for the rest of her life, and so the 'brothers' of Christ mentioned above were not her children, but those of her sister.
James the younger (the son of Alphaeus), was called the ' younger' to distinguish him from James the elder (the son of Zebedee) the brother of John the Beloved.
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Thrice-Blessed Pope Shenouda III of Blessed Memory