Yes, you can continue having sheepshead fish during pregnancy but, in moderation. Sheepshead is rich in vitamins and minerals. It is also a good source of folate, a nutrient essential to prevent serious birth defects of the spinal cord like spina bifida in your growing baby. The FDA categorizes sheepshead under fishes with medium levels of mercury. It is therefore advisable to limit the intake of sheepshead to 4 ounces a week and to make sure the fish is cooked properly before eating.