I'm sorry for your loss. If your children have SSNs, you list them on your return and claim them normally. No special procedure is needed. For the question "how long did the child live with you" answer "the whole year." This is the correct option in your situation. Answer no to any questions about support by other people or custody orders.
For children with Social Security Numbers, enter on the tax return as a dependent and answer the questions.
If your child was born and died in 2023 and didn't have an Social Security number you may enter "DIED" in column 2 of the Dependents section for the Social Security number. You won't be able to e-file, you will have to print and mail your tax return. You also need to attach a copy of the child's birth certificate, death certificate, or a hospital record showing a live birth.
Refer to the IRS FAQ and the TurboTax Help article Deceased dependent without SSN doesn't autopopulate DIED in the SSN field for instructions.
I am so sorry for your loss.