**Core Concept**
In primary open-angle glaucoma (POAG), the treatment goal is to reduce intraocular pressure (IOP) to prevent progressive optic nerve damage. The treatment of choice for prophylaxis of the fellow eye (right eye) in a patient with POAG in the other eye (left eye) is a topical medication that reduces IOP without causing significant systemic side effects.

**Why the Correct Answer is Right**
The correct answer is topical beta-blockers such as Timolol or Betaxolol. These medications work by reducing aqueous humor production in the ciliary body, thereby lowering IOP. They are effective in reducing IOP in the fellow eye and have a favorable side effect profile. The use of topical beta-blockers in the fellow eye is a common practice in glaucoma management to prevent the progression of disease in the unaffected eye.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option would be incorrect because the use of systemic carbonic anhydrase inhibitors is not the preferred treatment for prophylaxis of the fellow eye in POAG. Systemic carbonic anhydrase inhibitors can have significant systemic side effects, such as hypokalemia and renal stones.
* **Option B:** This option is incorrect because topical prostaglandin analogs, while effective in reducing IOP, are not typically used as prophylactic treatment in the fellow eye of a patient with POAG. They can be used in the affected eye, but their use in the fellow eye is not standard practice.
* **Option D:** This option is incorrect because oral beta-blockers are not typically used for prophylaxis of the fellow eye in POAG. Oral beta-blockers have systemic side effects and are not as effective as topical beta-blockers in reducing IOP.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the treatment of choice for prophylaxis of the fellow eye in POAG is topical beta-blockers, which can be used alone or in combination with other medications to reduce IOP and prevent disease progression.

**Correct Answer:** C.