Introduction
Asenath is the Egyptian wife of Joseph, daughter of Potiphera, a priest of On (an ancient Egyptian city associated with the worship of the sun god Ra), given to Joseph in marriage by Pharaoh as part of his elevation to high office in Egypt. She is the mother of Manasseh and Ephraim, the two sons Jacob later formally adopted as his own, becoming the ancestral figures of the half-tribes bearing their names.
Family
Marriage to Joseph
Genesis 41:45 records that Pharaoh gave Joseph Asenath, daughter of Potiphera, priest of On, as a wife, as part of the honours accompanying Joseph's appointment as administrator over Egypt during the years leading up to and through the famine.
Mother of Ephraim and Manasseh
Asenath bore Joseph two sons before the years of famine began: Manasseh, whose name Joseph explained as reflecting that God had made him forget his hardship and his father's household, and Ephraim, whose name Joseph connected to God making him fruitful in the land of his affliction.
Later Jewish tradition
A later, non-biblical Jewish text, Joseph and Aseneth, composed well after the Hebrew Bible and not part of its canon, considerably expands Asenath's story, including an account of her conversion from Egyptian religious practice before her marriage to Joseph; none of this material is found in the Genesis text itself.