New York's tax system is notoriously much more complicated that other states. Franchise taxes are handled by the New York Department of Taxation and Finance can be paid online or when filing through a software provider.
All LLCs, LPs and corporations need to pay franchise taxes in the State of New York.
"The easiest method is calculating tax based on net income, which equals the federal taxable income. A company's investment capital (minus any liabilities) may also be taxed. Another method is the minimum taxable income, calculated from net income plus some federal adjustments. Finally, the fixed dollar minimum method taxes companies on gross receipts, and charges set tiers a flat dollar amount."
Another breakdown of how taxes are calculated is available here. The MTA surcharge also applies to the franchise tax.
Franchise taxes in New York State needs to be paid annually, though companies can use estimated payments quarterly.
General business corporation calendar year filers must pay before April 15, whereas fiscal year filers must pay 3.5 months after the end of their last reporting period.
S corporations must file on or before March 15 or 2.5 months after the end of the last reporting period.