Is giving a gift or prize to some children but not others – because he memorized chapters of the Quran and exerted effort, while the other did not – considered prohibited favoritism?

It is obligatory to be equitable among children in giving gifts. However, it is permissible to favor one over others for a legitimate Sharia (definition)-compliant reason, such as need, illness, or if one of them is pursuing knowledge and striving diligently in it.

There is no harm in rewarding children for academic excellence or memorizing the Quran, because this is a preference based on a valid reason, not a pure favoritism. However, it is not permissible to single out some children for rewards while excluding others if they all exerted effort or succeeded. If they differ in memorization or excellence, the one who is less fortunate should not be deprived of a reward if they have put in their effort; rather, they should be rewarded. If some children do not have the aptitude for memorization or excellence, their other talents should be developed, encouraged, and rewarded.

To avoid the accusation of favoring some children, the father can tell his children: "Whoever does such and such will receive such and such gifts," and then reward the diligent one.