I say, and with God's success: It is not obligatory for the father to pay Zakat al-Fitr for his wealthy young son; because although he has full guardianship over him due to his young age, he is not obligated to provide for him due to his wealth, unlike his poor young son. Refer to: رد المحتار 2: 75، وبدائع الصنائع 2: 70-71، والوقاية ص230، والله أعلم.