What do I select if I am paying child support and taking care of my children but their mothers are claiming them?

[xmasbaby0]

You do not put anything about child support.  Child support is not deductible.  

Are you the custodial parent?  Do you have an agreement with the other parent to allow the other parent to claim them--due to divorce or that you live apart and share custody?  Did one of you sign a Form 8332?

If there is a signed 8332 then the custodial parent retains the right to file as Head of Household, get earned income credit and the childcare credit + education credits if the child is a full-time college student.  The non-custodial parent gets the child tax credit for children under the age of 17.

As far as the IRS is concerned, the custodial parent is the one with whom the child spent the most nights during the tax year--at least 183 nights.

If you are a non-married couple who live together then only one of you can claim the child(ren) and the one not claiming the child does not enter anything at all on their tax return about the child. 

[Hal_Al]

Simple answer: You do not enter the child, at all, in TurboTax (TT), if the mother is claiming the child.

As the other answer indicates, it can be more complicated than that, depending on the details of the situation. You haven't provided enough information to give you a more definitive answer.

Read on for all the rules.

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The custodial parent has first priority on claiming the children on her taxes; regardless of the amount of support provided by the non-custodial parent. The IRS goes by physical custody, not legal custody. The non-custodial parent can only claim the child as a dependent if the custodial parent gives permission (on form 8332) or if it's spelled out in a pre 2009 divorce decree. Even if a divorce decree, dated after 2008, gives the non-custodial parent the right to claim the child, he must still get form 8332 from the custodial parent. A properly worded decree should require her to provide that form. https://www.irs.gov/pub/irs-pdf/f8332.pdf

For tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent.

This may be helpful in your negotiations with the ex:

 There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.

Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.

 So, it's good idea to let the other parent know that you will be claiming those items, as many first time divorced parents are not aware of this rule and may try to claim those items, which will cause the IRS to send out letters.

Ref: https://www.irs.gov/publications/p17#en_US_2017_publink1000170897

Scroll down to "Children of divorced or separated parents (or parents who live apart)"

[Opus 17]

First of all, if you are living together in the same home as the other parent, then one parent lists the child on their tax return and answers no to the custody agreement question, and the other parent does not list the child at all. The special rules that I will discuss below only apply when the parents are divorced or separated and live in separate homes.

The only parent who has the automatic right to claim a child as a dependent is the parent or the child lives more than half the nights of the year. You don’t get credit for paying child support and you don’t get credit for taking care of the child during the day. If the child does not live with you more than half the nights of the year, you can’t claim anything on your tax return unless the custodial parent gives you a signed form 8332 dependent release.

On the other hand, if the child lives with you more than half the nights of the year, then you are the only parent with the automatic right to claim the child as a dependent, and the other parent cannot claim anything unless you give them a signed form 8332 dependent release. The IRS rules are based on where the child lives, not any custody order, and if the child’s living circumstances change from year to year then the parent who is allowed to claim them may also change even if the court orders don’t change.  

Form 8332 only transfers the child tax credit. The ability to use the child to qualify for head of household status or earned income credit or the dependent care expense credit can’t be waived, shared, or transferred.

If the child lives with you more than half the nights of the year, and you have an agreement at the other parent can claim the child, then you give the parent for sign form 8332. You list the child in your tax return and say that they live with you more than half the year and then answer yes that you will give the other parent the release form. TurboTax will print a release form for you to give to the other parent and TurboTax will include the child on your tax return for head of household status and earned income credit if you qualify.  The other parent must indicate in TurboTax that the child does not live with them and they will only claimed a dependent because of form 8332. The tax program will give them the child tax credit but will not claim the child for head of household or EIC, and they must mail the original signed form 8332 to the IRS after e-filing the rest of their return. If both parents follow the rules, this will not create a conflict and both parents will be able to e-file.