Who Is Most Entitled to the Care (Kafālah) of Children

Answer—and Allah grants success: The matter is disputed among the scholars. The scholars of the madhhab said: the father has priority regarding the male child, and the mother has priority regarding the female child. Al-Manṣūr bi-llāh, and Abū al-ʿAbbās transmitting from al-Hādī (peace be upon him), said: the father has priority regarding both.
And it is said: the girl remains with her mother, while the boy is with his father by day and with his mother by night.1
I say: What appears to me in this issue is that priority follows the child’s religious and worldly best interest. If the child’s religious and worldly benefit lies in accompanying his father, then the father has priority over the mother; and if his benefit is greater in accompanying his mother, then the mother has priority—this applies equally to male and female. If the interests are equal, then the mother’s right is greater than the father’s; she is more compassionate toward the child, and the child is more attached to her. Allah Most High said: “Let no mother be harmed through her child.” [Al-Baqarah:233]
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1