If you used the desktop CD/Download editions installed on your computer, the only copy of your tax data file and any PDF's will be on the computer where the return was created. TurboTax does not store online any returns completed using the desktop editions.
If you used desktop software downloaded/installed from a CD to your own computer, then the tax files are stored locally on your own hard drive or any backup device you used like a flash drive. They are not stored online. If you cannot recover them due to a hard drive failure, etc. you can get a free transcript from the IRS or for a fee of $43, an actual copy of your tax return.
The only way to open a tax return that's on your computer (a .tax20yy file) is with the CD/Download TurboTax software for the corresponding year. You cannot open it in the TurboTax Mobile App or with TurboTax Online.
If you no longer have the software, and you only need copies of the returns, you could try TaxPrinter. You send them your .tax file and they send you back a PDF of the tax return, which you can then print with Acrobat Reader. TaxPrinter has no connection with TurboTax. I have never used TaxPrinter, so I cannot make a recommendation. I'm just making you aware of it.
It's not clear what you mean by "the Turbo Tax app." Are you referring to the TurboTax Mobile App that you use on a phone or tablet, or to TurboTax Online, or to the CD/Download TurboTax software that you install on your Windows or Mac computer?