I am a student of a professional college. My father was not able to support me financially, so, I requested someone to help me. He agreed to help me and pay my college fee. He gave me the fee and told me to pay it. But there was time for paying and the amount is with me in an Islamic bank since one year, and I will pay my fee after few months, Insha Allah. Now, should I extract Zakah from this money?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If such an amount of money constitutes a Nisaab (i.e. the value of 85 grams of gold) by itself or with other articles of trade or wealth, and it is possessed for one lunar year, then you have to pay its Zakah, regardless of being allocated for paying fees of study.
Here is an exception to the above-ruling: if there is an agreement between you and the university to pay the fees in a period that is less than one lunar year, and then, after paying the fees the remaining amount will be less than the Nisaab, then the amount you have is not subject to Zakah, since it is a kind of debt.
Allah knows best.