**Core Concept**
Medullary carcinoma of the thyroid is a type of neuroendocrine tumor originating from the parafollicular cells (also known as C cells) of the thyroid gland. These cells are responsible for producing calcitonin, a hormone involved in calcium and phosphorus metabolism. The tumor's ability to produce calcitonin is a key diagnostic marker.

**Why the Correct Answer is Right**
Calcitonin is produced by the parafollicular cells of the thyroid gland and plays a crucial role in regulating calcium levels in the blood. In medullary carcinoma of the thyroid, the tumor cells often produce high levels of calcitonin, leading to elevated serum levels. This characteristic makes calcitonin a reliable tumor marker for diagnosing medullary thyroid carcinoma. The measurement of calcitonin levels in serum is used as a diagnostic tool to detect the presence of this tumor.

**Why Each Wrong Option is Incorrect**
**Option A:** TSH (Thyroid-Stimulating Hormone) is a hormone produced by the pituitary gland that regulates the production of thyroid hormones (T3 and T4) by the thyroid gland. It is not a specific tumor marker for medullary carcinoma of the thyroid.

**Option C:** T3, T4, and TSH are thyroid hormones and the hormone that regulates their production, respectively. While these hormones are produced by the thyroid gland, they are not specific markers for medullary carcinoma.

**Option D:** Alpha-fetoprotein (AFP) is a tumor marker associated with certain types of cancer, including hepatocellular carcinoma and germ cell tumors of the ovary and testis. It is not typically elevated in medullary carcinoma of the thyroid.

**Clinical Pearl / High-Yield Fact**
Medullary thyroid carcinoma can be associated with Multiple Endocrine Neoplasia (MEN) syndromes, particularly MEN 2A and MEN 2B, which are inherited conditions characterized by the occurrence of multiple endocrine tumors.

**✓ Correct Answer: B. Calcitonin**