**Core Concept**
The question is testing knowledge about vaccine contraindications in children with a history of seizures or convulsions. **Vaccines containing live, attenuated viruses** can pose a risk to individuals with compromised immune systems or a history of seizures, as the live virus can cause the disease or trigger a seizure.

**Why the Correct Answer is Right**
The measles, mumps, and rubella (MMR) vaccine is a live, attenuated vaccine that is contraindicated in children with a history of convulsions or seizures. This is because the live virus in the vaccine can cause the disease in individuals with weakened immune systems, including those with a history of seizures. **The measles virus can also cause encephalitis, which can lead to seizures**.

**Why Each Wrong Option is Incorrect**
* **Option A:** Meningococcal conjugate vaccine is a polysaccharide-protein conjugate vaccine, which is not contraindicated in children with a history of seizures.
* **Option B:** Influenza vaccine is an inactivated vaccine, which is safe for use in children with a history of seizures.
* **Option C:** Hepatitis A vaccine is an inactivated vaccine, which is also safe for use in children with a history of seizures.

**Clinical Pearl / High-Yield Fact**
Children with a history of seizures or convulsions should receive the MMR vaccine at an older age, ideally after the age of 12, when the risk of seizures is lower.

**Correct Answer:** C.