I was told I could claim my child every year by a tax man. IRS said I have the right, but I was told it is up to the judge and that it might be every other year. However, if I can show I spend more on my child than the child support I get, I should be able to claim my child every year.
Look to your custody judgment first. If it is silent and you are the sole custodial parent, then yes.
In most situations, if the child lives with you more than 51% of the time, you get to claim the tax deduction & more importantly, file as "head of household."
But your custody agreement may provide for something else, so take it out & read it carefully. If it doesn't say anything, then the tax deduction belongs to you, as the parent with custody.
Hope this perspective helps!