Must the Husband Pay Zakah on Wife's Jewelry?
Question

I would like to know: my wife has gold jewelry which was given to her from mother but I am not well off and I am in debt also so how should I pay zakat on it?
Praise be to Allah.Who pays Zakah on wife's gold?
The husband does not have to pay Zakah on the jewelry on his wife’s behalf, because the Zakah is only obligatory on the possessor of the wealth, and the possessor in this case is your wife, because she is the owner of the jewelry. So she has to pay Zakah on it, either from the jewelry itself or from its monetary value .
If her husband or someone else pays Zakah on her behalf with her permission, that is OK, and he will be rewarded for this voluntary action. 
Can the wife pay Zakah to her husband?
If the wife wants to give the Zakah on her jewelry or anything else to her husband who is in debt and cannot pay it off or who is poor, there is nothing wrong with that, because it comes under the general meaning of the verse (interpretation of the meaning): 
“As-Sadaqat (here it means Zakah) are only for the poor, and the needy…” [At-Tawbah 9:60] 
Indeed, there is the hope that she will have a multiple reward, because of the Hadith narrated by Al-Bukhari (1466) and Muslim (1000) from Zaynab (may Allah be pleased with her), the wife of `Abdullah (may Allah be pleased with him), who said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: `Give in charity, O women, even if it is from your jewelry.’ I went back to `Abdullah and said, `You are a man who has little wealth, and the Messenger of Allah (peace and blessings of Allah be upon him) has commanded us to give in charity. Go and ask him if that is acceptable, otherwise I will give my charity to someone else.’ `Abdullah said to me, `No, you go and ask him.’ So I went, and there I saw a woman from among the Ansar at the door of the Messenger of Allah (peace and blessings of Allah be upon him), wanting to ask the same question. We felt too shy to speak to the Messenger of Allah (peace and blessings of Allah be upon him). Bilal came out to us and we said to him, `Go to the Messenger of Allah (peace and blessings of Allah be upon him) and tell him that there are two women at the door asking whether it is acceptable for them to give charity (Zakah) to their husbands and the orphans who are in their care, but do not tell him who we are.’ Bilal went in to the Messenger of Allah (peace and blessings of Allah be upon him) and asked him, and the Messenger of Allah (peace and blessings of Allah be upon him) asked, `Who are they?’ He said, `A woman from among the Ansar and Zaynab.’ The Messenger of Allah (peace and blessings of Allah be upon him) asked, `Which Zaynab?’ He said, `The wife of `Abdullah.’ The Messenger of Allah (peace and blessings of Allah be upon him) said to him, ‘They will have two rewards, the reward of (upholding ties of) kinship and the reward of giving charity.’” 
Ibn Hajar (may Allah have mercy on him) said: “From this Hadith it may be understood that it is permissible for a woman to give Zakah to her husband. This is the view of Ash-Shafi`i, Ath-Thawri, the two companions of Abu Hanifah, one of the two reports narrated from Malik and from Ahmad.” 
And Allah knows best.