When we look into Abraham's family there were 3 candidates who could have received the promise and become the heir. The first was Eliezer who was Abraham's servant. Abraham was in old age and his wife Sarah was not able to have children so he wanted to set up Eliezer to become his heir. But God told Abraham that he would not become the heir but a child from his own body would become the heir (Genesis 15:4 - Then the word of the LORD came to him: "This man will not be your heir, but a son coming from your own body will be your heir.) So Sarah, Abraham's wife who believed God and his promise told Abraham to have a child with her servant Hagar to fulfill what God had said "A son coming from your own body will be the heir". Abraham did so and had a child with Hagar the maidservant and he was named Ishmael. According to God's promise a son from Abraham's body would be the heir, Ishmael should become the heir because he came from Abraham's body and he was also the first born son (Jewish law is that the first born son always receives the inheritance). But there was one more condition in order to become the heir. (Genesis 17:15 - God also said to Abraham, "As for Sarai your wife, you are no longer to call her Sarai; her name will be Sarah. I will bless her and will surely give you a son by her. I will bless her so that she will be the mother of nations; kings of peoples will come from her." Abraham fell facedown; he laughed and said to himself, "Will a son be born to a man a hundred years old? Will Sarah bear a child at the age of ninety?" And Abraham said to God, "If only Ishmael might live under your blessing!"). Abraham wanted Ishmael to receive the blessing and become the heir but God told him that the son who would become the heir would be born through his wife Sarah. So later Sarah bore a child with Abraham and they named him Isaac (Genesis 17:19 - Then God said, "Yes, but your wife Sarah will bear you a son, and you will call him Isaac. I will establish my covenant with him as an everlasting covenant for his descendants after him. But my covenant (promise) I will establish with Isaac, whom Sarah will bear to you by this time next year.")
Then we can see that the child who became the heir according to God's promise was Isaac. But what was it that made him become the heir? When we look at this story it is strange because Ishamel and Isaac were both born through Abraham's body, also Ishmael was the first born son, so naturally he should have become the heir. But, the determining factor into who became the heir was not the father Abraham, but the mother Sarah. Isaac became the heir because he was born from Sarah the free women according to God's promise (Sarah will bear you a son and I will establish my covenant with him).
But in Galatians it said that in order to belong to Christ and become heirs of the promise we have to be Abraham's seed and heir according to the promise. Isaac was the child and heir according to the promise because of his mother, the free women Sarah. Then what about us? (Galations 4:26 - But the Jerusalem that is above is free, and she is our mother. For it is written: "Be glad, O barren woman, who bears no children; break forth and cry aloud, you who have no labor pains; because more are the children of the desolate woman than of her who has a husband. Now you, brothers, like Isaac, are children of promise.)
Through our Heavenly Mother Jerusalem we are heirs according to God's promise and we can truely say that we are children of promise. All glory, thanks and praise to our Mother who is free and gives us eternal life.