It depends. First, decide who meets the rules to claim the child. See: Who can I claim as a dependent?
Second, check if the child appears on the mom's return on page 1 of Form 1040. If yes, then the father cannot claim the child unless the mom files an amended return.
If no, then if the father is not the custodial parent, he will need the mother to provide him with Form 8332 if the parents are no longer married. See 2019 Form 8332 and Instructions.
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