Only one parent can claim the dependent. One parent will be the custodial parent and the other will be the non-custodial parent. The custodial parent is the parent who spends the most number of nights with the child during the year. The other parent is the non-custodial parent.
There are tie-breaker rules if the child spends equally the same amount of nights with both parents.
It's possible for the non-custodial parent to claim some credits that come with having a dependent. The child won't be a dependent on both returns, however the dependent must be a qualifying child for both parents. The custodial parent will need to provide consent to the non-custodial parent with the Form 8332. This form will allow both parents to share some credits if eligible.
https://www.irs.gov/zh-hant/newsroom/claiming-a-child-as-a-dependent-when-parents-are-divorced-separ...
