Question: Did the Prophet Ibrahim (Abraham) have any children after Ishmael? Did he only have Isaac through Sarah?

Google; Abraham had eight sons. The record of these sons and their names are in the Book of Genesis. First he had Ishmael, who was the son of a slave woman--Hagar of Egypt was his mother. She was the slave of Sarah, Abraham’s wife. When Abraham was 99 years old, Sarah miraculously became pregnant at age 89; then Isaac was born. Ishmael hated Isaac; he was jealous of Isaac, because Isaac was not a slave child, but the special son of God’s promise. Abraham had another wife, Keturah. She had six sons by Abraham (Genesis 25). So of the eight sons of Abraham, only Isaac was the son of Abraham and Sarah; only Isaac was the son the God had promised. It is similar of the story of Joseph in Genesis; all the brothers hated Isaac, just as Joseph’s brothers hated him and sold him into slavery.

Early in Isaac’s life, Ishmael mocked and made fun of Isaac. Isaac was the first son of Abraham to be circumcised on the eighth day of his life. Ishmael had been circumcised at the same time as Abraham. Circumcision is first mentioned in Genesis 17; from then on, all of Abraham’s children and slaves had to be circumcised, even as Abraham himself was. Jews are still circumcised on the eighth day. All the sons of Abraham, except Isaac, are the fathers of the Arab nations. They are still circumcised at age 12 or 13.

(Comment)

— The Bible says that Abraham was 86 when Ishmael was born. He was 100 when Isaac was born so he had to be about 16 or so when he was sent away.

Why did God choose Isaac instead of Ishmael?

By choosing Isaac over Ishmael, God confirms that all people born of faith (as Isaac was born of his parents' faith in God's promise to do the impossible) are truly children of Abraham and thus heirs of the promise.

What did the angel say about Ishmael?

The angel of the LORD also said to her: "You are now with child and you will have a son. You shall name him Ishmael, for the LORD has heard of your misery. He will be a wild donkey of a man; his hand will be against everyone and everyone's hand against him, and he will live in hostility toward all his brothers".

What was God's promise to Hagar?

There, by a spring of water, she was found by an angel of the Lord, who told her to return home and promised her that she would have many descendants through a son, Ishmael; he would grow up to be a “wild ass of a man”, in constant struggle with all other men.

However, despite the early and later struggles of Isaac and Ishmael, they are the eventual founders of 12 (nations) princes each.

God told Abraham that He would establish his covenant through Isaac, and when Abraham inquired as to Ishmael's role, God answered that Ishmael has been blessed and that he "will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation". (Genesis 17).