All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
A Muslim has to pay Zakaah if his wealth meets two conditions:
1. It should constitute a Nisaab (the amount that determines whether Zakaah is obligatory or not. It is equal to the value of 85 grams of pure gold).
2. One Islamic (lunar) year should be passed after possessing the wealth; i.e., the Nisaab.
Thereupon, you are not obliged to pay Zakaah since your holdings do not constitute the Nisaab. May Allah reward you for your good support to your family.
For more benefit on Zakaah, please refer to Fataawa 165375, 401332, and 379973.
Allah knows best.