Hagar and Ishmael were cast out into the wilderness of Beersheba when Isaac was weaned. (Genesis 21)
When Abraham and Abimelech had a dispute over a well, Abraham set aside 7 ewe lambs as witness that he dug the well that Abimelech's servants seized. They made a covenant there, and that place was called Beersheba. Abraham planted a tamarisk tree there and called on the name of the Lord, the Everlasting God. (Genesis 21)
When Samuel was old, he appointed his sons Abijah and Joel as judges at Beersheba, but they are ungodly and take bribes. The elders wanted a king to judge them instead, so the LORD had his warn them what a king would take from them but ultimately give into their demands. (1 Samuel 8)
Then Jezebel sent a messenger to Elijah, saying, "So may the gods do to me and more also, if I do not make your life as the life of one of them by this time tomorrow." Then he was afraid, and he arose and ran for his life and came to Beersheba, which belongs to Judah, and left his servant there. (1 Kings 19:1-3)