Is it permissible to pay off the debt of a son who is in need when one has other children?

It is obligatory to treat one’s children fairly. See Question no. 22169. 

It is obligatory to treat children equally in gift-giving and it is forbidden to single some out for gifts or to show preferences, unless there is a compelling reason for doing so. 

If there is a reason to show preference to one or to single one out, then it is acceptable to do so, such as if one of them is sick, blind or disabled, or he has a large family, or he is a student, and other reasons. So in that case it is acceptable to give him preference for those reasons. 

Imaam Ahmad referred to that when he said – concerning singling out some of one’s children to be beneficiaries of a waqf – “There is nothing wrong with that if it is because of a need, but I regard it as makrooh if it is by way of showing favouritism.” 

Shaykh al-Islam Ibn Taymiyah said: “The hadeeth and the reports indicate that it is obligatory to treat children fairly… but there are two kinds: 

1 – Those who need him to spend on them in sickness and in health and so on, in which case fairness means giving each of them what he needs, and it makes no difference if he needs a little or a lot. 

2 – Needs which all the children will have in common, such as gifts, maintenance and arranging their marriages. Undoubtedly it is haraam to show preferences with regard to these matters.

From these two stems a third kind, which is helping out one child for an extraordinary need, such as paying off the debt of one child, or paying compensation on his behalf (if he has caused injury to another), or paying the mahr on his behalf, or giving him the money he needs for his wife’s maintenance, and so on. Concerning whether or not he is obligated to give a similar amount to the other children is subject to further discussion.” (From al-Ikhtiyaaraat)