بسم الله الرحمن الرحيم
If you own only 20 gram gold and you don’t have cash at all then zakah is not wajib on you. But if you have some extra money saved from your basic needs along the gold then zakah shall be wajib on you. Your husband is not liable to pay your zakah. You should pay your zakah yourself. However if your husband pays your zakah with your permission then it shall be valid. It should be noted that the ruling will apply in case he has given you the jewellery into your possession, not as loan only for use.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.