Some points.
A step-parent has the same legal right to claim a dependent as a biological dependent, and this right does not end if you divorce the biological parent.
The parent(s) who are automatically entitled to claim the child as a dependent are the parent(s) with whom the child lived more than half the nights of the year (183 or more nights).
In some cases, a child might live with both parents more than half the nights of the year (for example, if the parents separated in July). In that case, both parents have the right to claim the child as a dependent, and if they don't agree, the first tiebreaker is where did the child live the greater number of nights.
Here, if the biological father claimed the child as a dependent and you and your wife did also, the IRS will send notices of the duplicate claim. The first letter usually informs you of the problem and asks you to check your facts and gives you the opportunity to change your claim. If you don't (and assuming the father does not amend to remove his claim) then the next letter will ask for proof of where the child lived during the year. You will need to submit documents and other proofs showing that the child lived in your home more than half the year. The IRS likes documents from "authorities" best, like letters to your address from your child's school or doctor that show the school and doctor expected the child to be living with you. If there was a school bus schedule (pick up every day at your house except Wednesdays and alternate Mondays, for example) that will be very helpful. You could also think about including emails and text messages documenting the custody schedule and custody exchanges. Your goal, if it gets that far, is to show that the child lived in your home with you and your wife for more than half the nights of the year.
