Here's the evidence:

References to a brother named James

Mark 6:3

Is not this the carpenter, the son of Mary[a] and brother of James and Joses and Judas and Simon, and are not his sisters here with us?” And they took offense[b] at him.

Matthew 13:55-56

55 Is not this the carpenter’s son? Is not his mother called Mary? And are not his brothers James and Joseph and Simon and Judas? 56 And are not all his sisters with us? Where then did this man get all this?”

Galatians 1:18-19

18 Then after three years I did go up to Jerusalem to visit Cephas [a.k.a. Peter] and stayed with him fifteen days; 19 but I did not see any other apostle except James the Lord’s brother.

The first two are not definitely of importance, but last one almost certainly refers to James the Just, who became head of the Jerusalem Church after Jesus died, and here Paul explicitly identifies as "the Lord's brother"

General references to siblings or other family members:

Mark 3:20-21

20 and the crowd came together again, so that they could not even eat. 21 When his family heard it, they went out to restrain him, for people were saying, “He has gone out of his mind.”

John 2:12

12 After this he went down to Capernaum with his mother, his brothers, and his disciples; and they remained there a few days.

John 7:3-5

3 So his brothers said to him, “Leave here and go to Judea so that your disciples also may see the works you are doing; 4 for no one who wants[a] to be widely known acts in secret. If you do these things, show yourself to the world.” 5 (For not even his brothers believed in him.)

1 Corinthians 9:5

5 Do we not have the right to be accompanied by a believing wife,[a] as do the other apostles and the brothers of the Lord and Cephas?

Acts 1:14

14 All these were constantly devoting themselves to prayer, together with certain women, including Mary the mother of Jesus, as well as his brothers.

There is debate whether "brother" could also mean "half-brother" (from Mary, after Joseph died) or "step-brother" (from Joseph's unmentioned first marriage) or "male cousin" or "close compatriot" (this is especially used to explain "brother of the Lord"), but the plain reading of the text is just normal "brother". Most, but not all, contemporary Protestant and secular Biblical exegetes, who do not follow the doctinre of Mary's perpetual virginity, consider it to be "brother-brother". In light of the stuff on "Clopas" below, it seems plausible that maybe this James who is the brother of Joses/Joseph is a relative of Jesus's, but not necessarily a literal brother.

Making sense of James the Just

After the Resurrection, Jesus appeared to a James before the others (1 Corinthians 15:7). Which James? I don't know, but from this context, it could well mean James the new head of the Church. In early post-biblical histories, "James the Just" is identified as the post-apostolic head of the Jerusalem Church. Eusebius quotes Clement of Alexandria (150 CE-215CE), "This James, whom the people of old called the Just because of his outstanding virtue, was the first, as the record tells us, to be elected to the episcopal throne of the Jerusalem church." Eusebius, a favorite of the Emperor Constantine, wrote his famous Ecclesiastical History ("Historia Ecclesiastica") sometime in the late third century, relying on earlier written accounts. One of these accounts was Hegesippus, who survives in fragments (I believe actually only in Eusebius), and who probably wrote mid-second century, making him one of the earliest histories we have outside of the Christian Bible. Eusebius quotes Hegesippus as writing:

After the apostles, James the brother of the Lord surnamed the Just was made head of the Church at Jerusalem.

The Jewish historian Josephus has a line about James "the brother of Jesus who is called Christ", but there's a lot of debate about whether that's authentic or a later Christian addition to the text.

The material in the New Testament is the only witness we have to Jesus in the first century C.E. All other material comes later, but second century is pretty close. There are further references to relatives as church leaders after James would have been dead in Eusebius, but I'll let you read about that here. However, Eusebius argues that this James was the son of Joseph's brother Clopas (see below though note that there's no record in the Christian Bible about Clopas being related to Joseph).