There are a number of potential income tax issues to address concerning your children post-divorce. While alimony is an income tax deduction to you, and a taxable income time to your ex, child support payments are NOT deductible by you.

Another issue (and it wasn't clear which one you were addressing) is whether you can claim your children as an exemption on your federal and perhaps state income tax return. The exemption for the children is almost always addressed in the divorce agreement. Typically it allocates the exemptions to one parent, and sometimes provides rotation (e.g., you get all the children as exemptions in even years and your ex in odd numbered years). Check your divorce agreement.