No not through Turbo Tax. You can only efile the current year 2021. And you can't use Turbo Tax Online to do prior years.
You can buy the last 3 years of Turbo Tax here,
You will need a full Windows or Mac to install it on.
You will have to print and mail in prior year returns. And if you are doing more than 1 year, send each year in a separate envelope. Sometimes the IRS will just staple all the sheets together and miss a second return. Be sure to attach copies of your W2s and any 1099s that have withholding on them. Don't forget state. You have to mail federal and state in separate envelopes because they go to different places. Get a tracking number from the post office when you mail them for proof of filing.
Or if you have a simple return you can get the blank forms from the IRS and fill them in by hand for free. I have a list of some of the basic ones I can post direct links to.
Each tax year has to be filed separately using the forms for the specific tax year. They cannot be combined in any way--do not even put them in the same envelope when you mail them. Software for past years is available back to 2018. Any earlier years can only be prepared on paper forms by hand--and those refunds have been forfeited now.
The current online program can only be used for a 2021 return--no other year. And if you did not file a 2020 return you will have trouble e-filing 2021. When it asks for your 2020 AGI try using zero. If zero does not work then you have to print, sign and mail 2021.
TurboTax has software for 2018 onward. Software is no longer available from TurboTax for earlier years, nor would it be supported even if you find it on eBay, etc. Updates are not available. It is also too late to receive a tax refund for a tax year earlier than 2018---those refunds have been forfeited. BUT if you owe tax due you still have to pay with penalties and interest. There might be other software providers that have software for those years, but you will not receive refunds for the returns even if the forms show a refund.
It might be better for you to seek local paid tax help in a situation when you are several years behind in filing your tax returns. Do you even have all of the documents you will need to enter and show your income—like your W-2’s and any 1099’s?
Online preparation and e-filing for 2018 and 2019 and 2020 is permanently closed.
To file a return for a prior tax year
If you need to prepare a return for 2018, 2019 or 2020 you can purchase and download desktop software to do it, then print, sign, and mail the return(s)
You may also want to explore purchasing the software from various retailers such as Amazon, Costco, Best Buy, Walmart, Sam’s, etc.
Remember to prepare your state return as well—if you live in a state that has a state income tax.
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/state received the return.
Federal and state returns must be in separate envelopes and they are mailed to different addresses. Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.
Note: The desktop software you need to prepare the prior year return must be installed/downloaded to a full PC or Mac. It cannot be used on a mobile device.
If you are getting a refund, there is not a penalty for filing past the deadline. If you owe taxes, the interest/penalties will be calculated by the IRS based on how much you owe and when they receive your return and payment. The IRS will bill you for this; it will not be calculated by TurboTax.
You only have until April 18, 2022 to file a 2018 return and still receive a refund. If you file a 2018 return past that deadline, your 2018 refund will not be paid to you—it will be forfeited—the IRS will keep it.
Refunds for tax years 2017 or earlier have been forfeited and will not be paid to you even if shown on the tax return form. But if you owe tax due, you will still have to pay, and you will be billed later for the interest and penalties owed.
Since you are filing a late 2020 return, the IRS will not have a 2020 AGI in the system for you. When the 2021 software asks for your 2020 AGI so that you can e-file 2021, use “zero.” If you cannot e-file by using zero then you will have to print, sign and mail your 2021 return.