According to Islamic tradition, Moses was born into a family of Israelites living in Egypt.
When he was young
The ruling Pharaoh on the advice of his soothsayers, ordered the killing of all new-born Israelite males.
In the basket
To protect her son, Moses’s mother put him in a basket and set him adrift on the Nile. He was discovered by the Pharaoh’s wife, Asiya, who adopted him.
Finding out if Moses is a prophet
The Pharaoh was still wondering if this was the Israelite boy that would get him out of power, so he asked his advisers for advise. They told him to bring two bowls, one with fireballs and the other with gems. If he was a normal baby, he would go for the fire, if he was a prophet, he would go for the gems. Then they brought baby Moses and put him near the two bowls. Moses was reaching for the gems when God made his hands change direction and go to the fire. then’ like all babies, he swallowed the fire; therefore, he stammered.
Moses grew up as a member of the Pharaoh’s household, sleeping in the Pharaoh’s palace, and for some days of the week, he went to his mother’s house, where he learned about worshipping God.
Having to leave
One day when he was walking outside he saw an Egyptian in a fight with an Israelite, and went to the Egyptian and hit him, in the process killing him. When he found out what he did, he prayed to God for forgiveness. The next day, he saw the same Israelite in a fight with another Egyptian. When Moses refused, realizing that the Israelite was troublemaker, the Israelite mentioned what happened the day before. When the Egyptian heard, he ran into the palace. He then came out running, telling Moses that they planned to kill him and so Moses had to run.
After travelling in the desert for a long time, he arrived in Midian and came into the company of an old man (some Muslims say he was the prophet Shoaib). Who recognized Moses as a man of God. He arranged a marriage between Moses and his daughter (Zipporah in Biblical and Hebrew tradition) and then Moses worked for him for eight to ten years.