Last year's tax return my cousin claimed my 2 children. This year i am claiming my 2 children. I do not want anyone but myself claiming my children. Is there anyway i can find out if someone else used

The only way to find out if your children have been claimed on another tax return is to file your own return with them included as your dependents.  Then, if your child or children have been claimed already, your return will reject.  Your reject code will specify the reason and the dependent that caused the rejection.

From that point, there is not a way for you to find out or determine who included your children on their return.  You will only know that it has been done.

If you are the one that should be claiming them, then at that point you should file your return by mail, including your children on your return as your dependent.  The IRS will then examine both your return and the return of the other person and make a determination about which one is legally able to claim the children.  You would likely be contacted by the IRS for more information while they are investigating both returns.