If you live together and are each filing as married filing separately, then just don't list them. It avoids confusion.
If you are divorced or separated and live apart and share custody, then read the rest of the answer.
If the children live in your home more than half the year, you should say yes and then run the detailed interview for each child. Even if you are allowing the other parent to claim the dependent for the child tax credit, there are some tax benefits that always stay with the parent who has custody more than half the year, that can't be waived, transferred or shared. This includes head of household status, EITC, and the dependent care credit.
If you are the parent who had custody more than half the year, enter the children as dependents, answer the questions, and say "yes" that you are allowing the other parent to claim them as dependents. The children will be listed on your tax return for certain benefits, but not the child tax credit. You must also give the other parent a signed form 8332 dependent release, allowing the other parent to claim the children even though they don't live with her.
https://www.irs.gov/forms-pubs/about-form-8332
If the children live with you and you just leave them off, and allow your ex to claim them as if they lived with her all year, she will be able to claim HOH and other tax benefits, which is tax fraud, and you may lose out on those benefits or pay higher taxes as single instead of head of household.
On the other hand, if the children do not live with you more than half the year, you can never claim them unless you have a waiver signed by the other parent. You can try answering that you support someone, but if you answer the questions honestly, the program will tell you they are not your dependents.
