If you lived with your child more than half the year (the child slept in the same home where you lived for more than 183 nights) then you as the parent have automatic first right to claim the child as a dependent.
If the child also lived in the home with a grandparent for more than half the nights of the year, the grandparent can claim the child as a dependent if the parent agrees and if the grandparent's taxable income is higher than the parent's taxable income.
If you did not claim your child as a dependent, you can file an amended return to claim your child and possibly claim additional tax refunds, if you are eligible for the child tax credit or EIC. The IRS will red flag the duplicate dependent claim and both you and your father will get letters asking you to justify your claim of the dependent. In this situation your father's claim will eventually be denied (after a 1-2 year investigation -- the IRS is not speedy) and he will owe back taxes with penalties and interest.
Depending on your various financial circumstances, you might get much less of a refund for your child than your father will have to pay back -- exactly who gets the best deal is not always obvious or easy to calculate and you have to test different scenarios in the tax program.
While you are entitled to claim your child, filing an amended return will likely harm your relationship with your father even more than it already is. You don't have a tax problem, you have a family problem. You may want to sit down and talk this out, possibly with the assistance of a social worker, pastor, or other trusted person.
