Thanks for your question.
To answer your question properly, I would have to know which Joseph you mean. Let's go through them in order:
Joseph the son of Jacob and Rachel: his story is recorded from Genesis 30:24 to the end of the book. In fact, the last verse of the book of Genesis deals with Joseph. He is one of the very best "types" of the Lord Jesus Christ found in the Bible. He was beloved of his father, hated by his brothers, sold by them into the land of death (Egypt), where he rose from the prison house to sit at the right hand of the king and became the saviour of his brethren. They didn't recognize him at their first encounter but as Stephen puts it in Acts 7:13 he was made known to them "the second time" just as our Lord will at his second coming.
Joseph is used of some other individuals in the Old Testament about whom we know little other than their names. The term "Joseph" is also used to describe the tribes of Ephraim and Manasseh, so named for the sons of Joseph. Because he became the heir after Reuben disgraced himself, Joseph was entitled to a "double portion" of Jacob's inheritance so the two tribes named after his sons are sometimes collectively referred to as "Joseph." See Ezekiel 47:13; Amos 5:6,15; Psalm 80:1 (Benjamin is also included because he was the only son of Rachel beside Joseph so Benjamin is more closely related to Ephraim and Manasseh than to the other tribes whose patriarchs were only half-brothers). Eventually, "Joseph" became a synonym for the northern kingdom of Israel as distinct from the southern kingdom of Judah (which was actually composed of Judah and Benjamin). Zechariah 10:6.
Joseph the step-father of Jesus: he is introduced to us in Matthew 1:16. His father's name was Heli [see Luke 3:23]
Joseph of Arimathea: Matthew 27:57-59 The wealthy member of the Sanhedrin (seems to have been a friend of Nicodemus John 19:38) who although secretly a disciple while Jesus was alive, courageously stood up to take care of the body of Jesus after his crucifixion. All the other disciples had fled and only he and Nicodemus publicly stood by their Lord - they had courage when it counted! We don't know who his father was.
Joseph Barsabbas: One of the potential replacements for Judas along with Matthias as recorded in Acts 1:23. Again, his parentage is unlisted.
I hope that answers your question.
God bless and keep you!