Short answer: You can't do that.
Long answer: The only time it is permissible to "split" the benefits of claiming a dependent is with the other parent when you are separated or divorced and living apart. Otherwise, you can't do that.
If you and your child live with your father, then your father can only claim the child as a dependent if his taxable income is higher than yours. And, whoever claims the child (you or your father) must claim all the dependent benefits, including head of household filing status, EIC, the child tax credit, and the dependent care credit. Those benefits can't be split or shared.
