Is it permissible to pay more than the Zakat al-Fitr amount for my disabled son?

The fundamental principle is the obligation to be just among children in giving gifts, based on the Prophet's (peace be upon him) saying: "Fear Allah and be just among your children." However, it is permissible to single out some children for a gift due to a reason that necessitates it, such as need, chronic illness, large family, or preoccupation with seeking knowledge. Therefore, there is no harm if the questioner prioritizes his mentioned son in giving charity on his behalf, with the recommendation that this be done secretly to avoid envy and discord among siblings.