My ex husband stated he filed a quit deed on our mutual property but there is no record of quit deed

Your starting point is the language of your divorce settlement agreement or final judgement of divorce. If the agreement or court order required your husband to transfer title to the properties from joint name into his name alone and that same was to be accomplished by a specific date, you need to follow up with the lawyer who represented you in the divorce to find out if those things were accomplished. If your ex-husband was obligated to transfer the titles to those properties into his name alone under the terms of your divorce agreement or court order and he failed to do so, then you may need to take action in the NJ family court system to compel him to do so or to be responsible for the tax liability incurred by you as a result of his failure to transfer the titles as required. If the agreement or court order required him to transfer the titles into his name alone and he failed to do so, a judge has the authority to hold him liable for the financial consequences of his inaction by making him pay for your tax liabilities and the legal fees for the necessity of the application). A very different issue is presented if you and he never had a writing in place requiring him to transfer title to the properties into his name alone after the divorce. In that setting, it is tougher for a judge to require him to pay for your tax liabilities on those properties when there is nothing in writing to require him to do so. If the "agreement" to transfer title from joint name into his name alone is not in the settlement agreement or court order, then you need to check your emails and your text messages to see if you have anything from him confirming his agreement to transfer title into his name alone.  If you have that in a text message or email, bring that material to a family law specialist so that he can figure out whether he has sufficient information to file an application with the court for relief on your behalf.