**Core Concept**
The supporting cells of the testis play a crucial role in the development and maintenance of spermatogenesis. These cells provide structural support, nourishment, and protection to the developing sperm cells.

**Why the Correct Answer is Right**
The correct answer is Sertoli cells, which are specialized somatic cells that provide a complex network of cytoplasmic extensions (tubuli) to support the developing sperm cells. Sertoli cells are responsible for the nourishment and protection of sperm cells through the provision of nutrients, hormones, and growth factors. They also play a key role in the regulation of spermatogenesis by controlling the release of sperm cells into the seminiferous tubules. The Sertoli cells are also involved in the production of androgen-binding protein (ABP) which helps in maintaining the high concentration of testosterone in the seminiferous tubules.

**Why Each Wrong Option is Incorrect**
* **Option A:** Leydig cells are not the primary supporting cells of the testis. While they do play a crucial role in the production of testosterone, they are not directly involved in the support of developing sperm cells.
* **Option B:** Peritubular cells are a type of smooth muscle cell that surrounds the seminiferous tubules and helps in the contraction of the tubules to move sperm cells towards the epididymis. However, they are not the primary supporting cells of the testis.
* **Option D:** The correct answer is not provided, but based on the options given, it is likely that the other option is Sertoli cells, which are the correct answer.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that Sertoli cells are responsible for the regulation of spermatogenesis and the production of androgen-binding protein, which is crucial for maintaining the high concentration of testosterone in the seminiferous tubules.

**Correct Answer:** C. Sertoli cells.