Praise be to Allah.
What is required of you is to spend on your son, on a reasonable basis, which includes his food, drink, clothing, medical treatment, school expenses and shelter, if his mother does not have accommodation of her own to share with him.
It is not permissible for you to give your zakaah to your son, because in that way you are saving your own wealth that you should be paying on his maintenance.
There is no differentiation between zakat al-fitr and other types of zakaah.
Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (2/269): Zakaah cannot be given to parents or children. Ibn al-Mundhir said: The scholars are unanimously agreed that it is not permissible to give zakaah to parents in cases where the one who is giving it to them is obliged to spend on them, because giving his zakaah to them will mean that there is no need for him to spend on their maintenance and he would no longer be required to do that, so the benefit of that would come back to him, and therefore it is as if he is giving it to himself.
Similarly, he should not give it to his child. Imam Ahmad said: He should not give zakaah to his parents, his children, his son’s son, his grandfather, his grandmother or his daughter’s son. End quote.
It is permissible to give zakaah to one’s ex-wife after the ‘iddah has ended, if she is poor and does not have sufficient maintenance from a relative of hers.
It says in Haashiyat Qalyoobi wa ‘Umayrah (3/197): The one who has sufficient maintenance from a relative or spouse is not regarded as poor according to the more correct opinion, because he is not in need, such as one who earns every day sufficient enough to meet his needs. End quote.
However, during the ‘iddah, a divorced woman comes under the same ruling as a wife, and it is not permissible to give zakaah to her.
See also the answer to question no. 146241.
And Allah knows best.