Well...a couple things:
1) NY e-files aren't expected to be ready until after 9 January...so they may be marked such for that....and maybe the forms are just the preliminary ones right now.
ANDDDD
2) NY strongly encourages e-filing, and may not want anyone print-filing until later.....so the forms, preliminary or not, may contain those marks until later in January. In fact, the State Availability documents for TTX show that the final NY forms for printing will not be ready until after 23 January
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See/navigate to the NY State availability chart here:
Intuit App
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*