Someone claimed for my child on their income tax without permission an I would like to know who did

You can't - the IRS won't release such information as it is considered private. If you feel that you are entitled to claim your child as your dependent, then do so. If the other person filed before you then you will not be able to file electronically but will have to file a paper copy instead. The IRS will investigate to see who is rightfully allowed to claim your child. To help that along, I suggest you attach a statement to your return that you are the custodial parent.