Can I still claim my children even though I'm not court ordered to pay child support but I still help financially the care taker doesn't want me to claim since they do

[DoninGA]

If you are not the custodial parent, meaning the children are living in your home for over 6 months of the year, you cannot claim them as dependents.  You would only be able to claim them as a dependent if the custodial parent gave you a Form 8332 releasing their claim on the children as dependents.