Can epilepsy medication have adverse effects on the baby?

Yes: Most antiepileptics increase the rate of birth defects when used in the first trimester, but the overall rate is still fairly low (increases from baseline of about 1% to about 3%). Importantly, antiepileptics may still be required if there are uncontrolled seizures. One can't avoid them if one is seizing without them. Uncontrolled seizures are more dangerous than the drugs.

All have risk.: During pregnancy your blood level of seizure medication causes a blood level in the baby. All aeds have risk for malformation and development problems. Just having epilepsy also increases risks. However, having seizures while pregnant is even worse. Take your usual med, take folate, (folic acid) and get frequent checkups.