Here we find that God will bless Sarah and give Abraham a son. It's very important to recognize that even though Abraham and Sarah already had a son, God did not acknowledge Ishmael, as their son. This was due to Abraham and Sarai attempting to circumvent God's will, by not waiting on God to deliver on his promise and having a son by Hagar, their handmaiden. In God's eyes, Ishmael was an illegitimate son. However, God did not condemn Ishmael, he promised to make him a great nation, through 12 princes.
Most scholars now believe and support that all Arabic people are from Ishmael. Islam proudly proclaims that supposition. However, does the text and historical records support that?
The Biblical record of Ishmael gives us the names of the 12 sons, but no clue as to how they might be connected to the modern Arabic Tribes. This list is given in Genesis 25 and later repeated in I Chronicles 1:29-33.
"Now these are the generations of Ishmael, Abraham's son, whom Hagar the Egyptian, Sarah's handmaid, bore unto Abraham: And these are the names of the sons of Ishmael, by their names, according to their generations: The firstborn of Ishmael, Nebajoth, and Kedar, and Adbeel, and Mibsam, and Mishma, and Dumah, and Massa, Hadad and Tema, Jetur, Naphish and Kedmah. These are the sons of Ishmael, and these are their names, by their towns and by their encampments; twelve princes according to their nations." Genesis 25:12-16
and later repeated in I Chronicles 1:29-33.
"And these are their generations: the first-born of Ishmael, Nebaioth, then Kedar, and Adbeel, and Mibsam, Mishma, and Dumah, Massa, Hadad, and Tema, Jetur, Naphish, and Kedemah. These are the sons of Ishmael."
These sons eventually took wives, had children, and through these children, tribes were formed. These tribes made up the nations that dwelt from Havilah to Shur, and from Egypt to Assyria. The descendants of Ishmael, however, were not the sole tribes in the Arabian Desert. Other tribes emerged from other sources. Some of these, such as the tribe of Qarish, became the people of South Arabia along with others who wandered and settled in Arabia.
Islamic Apologists attempt to link Mohamed to Hadad, the eighth son of Ishmael. However, historical records show that Mohamed was born of the Qarish tribe, which were not of the Ishmael lineage. The tribe of Qarish conquered the tribe of Fihr ibn Malik, which was of the lineage of Ishmael. Therefore, there isn't any generational connection, with the sons of Abraham. Ishmael is not the Father of Islam.
As for Isaac, he was the promised legitimate son of Abraham.