Teachers at New York City Public Schools must hold work authorization status. This means that you must have citizenship, residency, or a work visa that allows you to work in the United States.
Note that there are limited work visa sponsorship opportunities available through NYCPS schools. These opportunities are only available for candidates who hold New York State Education Department teaching certification in high-need subject areas as determined by NYCPS. Additionally, candidates are required to identify a NYCPS school that wishes to hire them and will cover the costs of their work visa sponsorship. See here for more details.