"Won't that work to apply to my daughters inherited IRA?"
That won't work for an inherited IRA. TurboTax has no capability for you to even enter the basis in an IRA inherited by a non-spouse beneficiary.
"Since I have entered the non-deductible contributions on the 2023 return, how will TurboTax handle this in future years? Will TurboTax recognize that I have entered it already?"
If you are asking in regard to the basis in the IRA inherited by your daughter, as I said, there is nowhere in TurboTax to enter that. It must be tracked on Forms 8606 prepared outside of TurboTax.
If you are asking about nondeductible contributions made to your daughter's own (not inherited) IRAs or your own IRAs, TurboTax will track that and prepare Form 8606 to report new nondeductible traditional IRA contributions and to calculate the nontaxable and taxable amounts of traditional IRA distributions. Once applied to a distribution the basis is no longer in the individual's traditional IRAs, reducing the basis remaining in the individual's traditional IRAs.
To be clear, except when a spouse beneficiary rolled an inherited IRA over to their own IRA or assumes ownership, the inherited IRA is still an IRA of the decedent but maintained for the benefit of the beneficiary.
