Yes, as long as you otherwise qualify. Please see this FAQ which describes in more detail this credit: https://ttlc.intuit.com/replies/3301418
Your child's father cannot claim the credit because he is not the custodial parent. His payments for daycare will be considered similar to if he were paying child support: nonreportable and nontaxable gifts. Thus, the payments he is making are considered to be made by you. If you otherwise qualify (child is under 13 and you have earned income from work, and you use daycare because you are working), you and only you will be able to deduct this expense on your return.
**Say "Thanks" by clicking the thumb icon in a post. **Mark the post that answers your question by clicking on "Mark as Best Answer"