Thank you for the question on the descendants of Mary and Joseph, “Are there descendants of Mary and Joseph?”
The Catholic church teaches that Mary and Joseph had only one child, Jesus and no other children. The other children mentioned in the Scriptures are referred to as cousins if my understanding of Catholic teaching is correct.
As a student of the Scriptures, the Scripture refers to other children of Mary and Joseph. For one’s consideration, here are some passages:
A. Matthew 12:46–50, (Mark 3:31–35, Luke 8:19–21)says this, “While Jesus was still talking to the crowd, his mother and brothers stood outside, wanting to speak to him. 47 Someone told him, “Your mother and brothers are standing outside, wanting to speak to you.” 48 He replied to him, “Who is my mother, and who are my brothers?” 49 Pointing to his disciples, he said, “Here are my mother and my brothers. 50 For whoever does the will of my Father in heaven is my brother and sister and mother”(A searchable online Bible in over 150 versions and 50 languages). Citations are from the New International Version.
B. Mark 6:1–3 says this, “Jesus left there and went to his hometown, accompanied by his disciples. 2 When the Sabbath came, he began to teach in the synagogue, and many who heard him were amazed. “Where did this man get these things?” they asked. “What’s this wisdom that has been given him? What are these remarkable miracles he is performing? 3 Isn’t this the carpenter? Isn’t this Mary’s son and the brother of James, Joseph, Judas and Simon? Aren’t his sisters here with us?” And they took offense at him” (NIV).
It is possible to interpret the brothers and sisters as cousins of Jesus, but it unlikely that the the cousins would be following Mary. They would be following their own father and mother. The words of Mark 6 by the towns people would at least imply more than just cousins since they were very familiar with them. If Mary and Joseph had other children, there would be six that is mentioned with four brothers and the referral of sisters would mean at least two daughters of Mary and Joseph.
It would be reasonable to assume that the brothers and sisters of Jesus married and had children of their own. Thus there would be descendants of Mary and Joseph. Can one trace the lineage of the brothers and sisters to Mary and Joseph. That may be difficult since Jesus was not fathered by Joseph but by the Holy Spirit. The New Testament traces the lineage of Joseph through the Gospel of Matthew and Mary through the Gospel of Luke. There is no indication that Jesus was married as it is likely that the siblings of Jesus had a difficult time believing or seeing him as someone who is that much greater than themselves. The reference of Jude is debated whether he was the brother of Jesus or not (Jude vs. 1).
Are there any living descendants of Mary and Joseph? With the destruction of Jerusalem in 70 CE, the Jewish people were scattered for the most part. Could there be living descendants of Mary and Joseph? I would not rule that possibility out but I have no evidence for it. The Jews desired to keep their genealogy to trace back to Abraham, if all possible.
SUMMARY: It is likely that there may be some descendants of Mary and Joseph that are still living today since they had six other children. That is just my personal opinion, not based on evidence.
For more perspectives:
https://www.quora.com/Are-there-descendants-of-Mary-and-Joseph