Is it permissible for a father to pay off the debt of one of his poor children from his own money, while maintaining justice among his children?

Justice must be observed among children in giving gifts, and تخصيص (designating) or تفضيل (preferring) one over others is forbidden, unless there is a compelling reason for it, such as one of them being ill, or having a disability, or having a large family, or being a student of knowledge. In such cases, there is no harm in preferring them. Imam Ahmad indicated the permissibility of preference due to need, not out of selfishness (اثارة). Sheikh al-Islam Ibn Taymiyyah explained that justice in spending (نفقة) means giving each what they need, and that differentiation (تفاضل) is forbidden in matters where needs are shared, such as gifts, sustenance, or marriage. There is a third type, such as settling a debt or giving a dowry, where giving the same to another is debatable.