You generally can't e-file a prior year.  To file your 2015 return, you will need to mail a printed copy to the NY tax department.  If you don't have a printed copy, you will need to install turbotax on your own computer, since turbotax online can only prepare the current year (2016).

If you paid to file online but never finished, you can contact customer support for a download to install the program.  If you did not pay before, you will need to purchase turbotax for 2015.  Look at the bottom of the turbotax home page for "past year programs".