You probably cannot deduct it. It's not clear what kind of extracurricular activity you are talking about, who runs it, who you are paying, or exactly what you are paying for. Are you thinking of deducting it as a charitable contribution or as a child care expense?
Any payment for your child to participate in an activity is not deductible as a charitable contribution, even if the organization that you make the payment to, and that runs the activity, is a tax-exempt or charitable organization. For example, if you make a contribution to the Boy Scouts and you get nothing in return, that's a deductible contribution. But if you pay for your child to participate in Boy Scout activities, that is not deductible.
It doesn't sound like a child care expense either. Child care is not the primary purpose of the activity. The purpose is to participate in the sport, club, or whatever the activity is. (Since you use the term "extracurricular activity," I am assuming that the child is in kindergarten or higher.) And you have to meet other requirements to claim a deduction for child care. One of the requirements is that you are paying for the child care so that you can work.
The fact that an organization gives you its tax ID number does not mean that any payment you make to that organization is tax deductible.
