TurboTax software is available as far back as 2016. If you prepared your federal returns using TT then you can go back and prepare the state returns from those years. It will require the purchase and download of desktop software for each of those years. The returns must be printed, signed and mailed to the state in separate envelopes for each year.
If you are behind for farther back than 2016, you could try downloading the forms from the state's website to prepare by hand, or seek local paid tax help.
To finish a prior year return started in TT online:https://ttlc.intuit.com/questions/2559403-how-do-i-finish-a-prior-year-return-that-i-started-in-turb
Online preparation and e-filing for 2016 - 2018 is permanently closed. You have to download 2016 - 2018 software to a full PC or Mac (not to a mobile device) and then print, sign and mail your return. If you already paid for your TurboTax software, you can contact customer support to push a download of the software to you.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS and/or your state received the return.