Answered by Shaykh Amjad Rasheed
I pay money to the mosque for its maintenance and to help pay off its debt, so does that money count as paying zakat?

The money that is paid to fulfill the needs of the mosque does not count as zakat since it is not permissible to spend the mandated zakat except on the eight groups of recipients who are mentioned in the Qur’an, according to His saying, {Verily, charity is for the poor, those short of money, zakat workers, those whose hearts are to be reconciled, those purchasing their freedom, those in debt, the path of Allah and those fighting for Allah}.
Spending in the path of Allah means jihad only. It does not mean every path to good.’ This is the position of four schools of Sunni law, and the position of the overwhelming majority of Islamic scholarship. This the money that is paid for the mosque’s maintenance and paying off its debts does not count as zakat; rather, it is in itself praiseworthy charity.