Is a father carrying his child and helping his wife in childcare—especially when she is ill or tired—considered a religious duty and a responsibility upon him, or is it a favor and kindness from him, and is a father sinful if he refuses to carry the child without reason?

Raising children is a shared responsibility between spouses, encompassing education, discipline, and protection from corruption. As for working outside the home and providing for the family, that is the husband's responsibility, while service within the home is the wife's responsibility, and this includes preparing food, cleaning the house, and caring for the children. Indeed, Fatimah was assigned the internal service (household chores), and Ali was assigned the external service. Caring for and carrying the child falls under internal service. If the wife is sick or tired, she should not be burdened beyond her capacity, and the husband should do it himself or hire someone to do it. Both spouses should cooperate in kindness, and the man should help his wife with household chores, especially when she is tired.