When e-filing after the due date the system will only allow you to enter the date you are e-filing. 

New York City is one of the few state/local agencies that didn't push back the deadline, they have special provisions to request that penalties for late-filed extension and returns can be waived. 

More information can be found here: 

https://proconnect.intuit.com/taxprocenter/tax-law-and-news/is-the-tax-deadline-delayed-what-to-know...