I say, and with God's success: The father should pay Zakat al-Fitr for his young child if he is poor; because the father's obligation to provide for his son is mandatory, and the father's guardianship over him is complete. In contrast, he does not pay for his wealthy young child. Ibn Umar, may Allah be pleased with him, said: 'The Messenger of Allah (peace be upon him) commanded Zakat al-Fitr to be paid for the small and the large, the free and the slave, from those you support.' This is found in Sunan al-Bayhaqi al-Kabir 4: 161, Sunan al-Daraqutni 2: 140, and Musnad al-Shafi'i p. 93. Refer to Bada'i al-Sana'i 2: 70-71, and Allah knows best.