My father expired before 10-years, I'm only care taker of my mother. My question is that my mother has some gold with her so I've to pay Zakaah for that savings.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

If the gold that your mother possessed is kept for saving and spending, then Zakat has to be paid on it. But if it is only kept for use, the scholars are of the view that there is no Zakat on jewellery that is used as an adornment as per Fatwa 82925. However, some other scholars are of the view that Zakat has to be paid on jewellery used as an adornment so it is better to pay in order to be on the safe side. Please refer to Fatwa 81332 for the amount of Zakat on gold.

So, if your mother opts for the safe side and wants to pay Zakat, she is obliged to pay Zakat on herself, i.e. from her own wealth but there is no harm on you to pay the Zakat for her out of your own wealth provided that you inform her and she agrees so that she intends to that effect [to pay the Zakat] as the intention of paying Zakat is a condition for Zakat to be acceptable. The Prophet said: "Indeed actions are judged according to their intentions. So every one will be rewarded for what he intends."  [Al-Bukhari and Muslim]

Allaah Knows best.