No, you and your spouse cannot both claim your son as a dependent on your separate returns. According to the IRS rules, a child may only be claimed as a dependent on one return in a tax year. If both parents claim a dependency deduction for the child on their income tax returns, the IRS will treat the child as the qualifying child of the parent with whom the child resides for the longer period of time during the taxable year. If the child resides with each parent for the same amount of time during the taxable year, the IRS will treat the child as the qualifying child of the parent with the higher adjusted gross income (AGI).
Additionally, the special rules for children of divorced or separated parents (or parents who live apart) specify that the child is generally treated as the qualifying child of the custodial parent, which is the parent with whom the child lived for the longer period of time during the year. The noncustodial parent can only claim the child as a dependent if the custodial parent signs a written declaration (Form 8332) releasing the claim to the exemption, and the noncustodial parent attaches this form to their return.
Therefore, only one of you can claim your son as a dependent, and you must determine which parent qualifies based on the time the child lived with each parent or the higher AGI if the time is equal.
Sources:
IRS FAQ
Publication 501 (2023)
§ 152. Dependent defined
Publication 1380
Publication 504 (2023)
