Do I list my child as a dependent even though his father is claiming him this year?

When asked if I support someone else (my son) I selected yes. I am unsure how to proceed to make sure that his father and I aren't both claiming him this year. I do have childcare costs to claim, but am unable to do so if I remove my son as a dependent.
Do I just remove him as a dependent altogether even though we have 50/50 custody?