The cost basis in an inherited IRA must be kept separate from any cost basis you have in your own IRA and must be reported on a separate 8606 form that must be manually prepared and attached to a mailed tax return. TurboTax can only prepare a 8606-T for the taxpayer, or a 8606-S for the spouse, but not for an inherited IRA.
Unfortunately TurboTax does not support a 8606 for an inherited IRA. When you enter a 1099-R with a 4 in box 7 and the IRA box checked, TurboTax will ask if there was a non-deductible basis in the IRA. When you say yes then you must enter the calculated taxable amount from line 15 from a manually prepared 8686 form. You would use the new 8606 line 14 amount to carry forward to next year.
Form https://www.irs.gov/pub/irs-pdf/f8606.pdf
Instructions https://www.irs.gov/pub/irs-pdf/i8606.pdf
Enter your E-mail address. We'll send you an e-mail with instructions to reset your password.