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. 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 they spend the night then it counts as time lived with the other parent, not you.
More than half the year to the IRS means 184 nights or more (in a leap year - 183 nights in non-leap year) that do not need to be consecutive.
See Custodial parent and noncustodial parent in Pub 501
You have to count the days. Keep a calendar. Actually you have to count the nights. If they sleep at your home that counts as a day that they lived with you. If they sleep at Dad's home it counts as a day that they lived with him.
The number of months that you enter in TurboTax is not precise. It's the days (or nights) that matter, not the months. If they lived with you more than half the nights during the year, enter 7 months or more. If they lived with you less than half the nights during the year, enter 5 months or less.