Among all the world's religions, Jews, Christians, and Muslims all claim Abraham as being their father. How does God's word define who is a child of Abraham?

1. Jesus is speaking to Jews somewhere in the temple. How doe Jesus define who a child of Abraham is?

They answered and said to Him, "Abraham is our father." Jesus said to them, "If you are Abraham's children, you would do the deeds of Abraham. But now you are seeking to kill Me, a man who has told you the truth, which I heard from God. This Abraham did not do. You are doing the deeds of your father." They said to Him, "We were not born of sexual immorality; we have one Father: God." Jesus said to them, "If God were your Father, you would love Me, for I proceeded forth and have come from God, for I have not even come of Myself, but He sent Me. Why do you not understand what I am saying? It is because you cannot hear My word. You are of your father the devil, and you want to do the desires of your father. He was a murderer from the beginning, and does not stand in the truth because there is no truth in him. Whenever he speaks a lie, he speaks from his own nature, for he is a liar and the father of lies. (John 8:39-44, LSB)

2. What is the apostle Paul saying? What do you observe that explains: a) not all Israel are of Israel, and b) not all are children of Abraham because they are the seed of Abraham? How do you understand: a) in Isaac your seed shall be called, and b) the children of the promise are counted as the seed?

But it is not as though the word of God has failed. For they are not all Israel who are descended from Israel; nor are they all children because they are Abraham's seed, but: "through Isaac your seed will be named." That is, the children of the flesh are not the children of God, but the children of the promise are considered as seed. For this is the word of promise: "At this time I will come, and Sarah shall have a son." (Rom 9:6-9, LSB)

3. What do you observe Paul saying about Abraham's seed?

There is neither Jew nor Greek, there is neither slave nor free man, there is no male and female, for you are all one in Christ Jesus. And if you belong to Christ, then you are Abraham's seed, heirs according to promise. (Gal 3:28-29, LSB)