**Core Concept**
The question involves the management of a child patient with leukemia, specifically the treatment of a periapical abscess. Leukemia is a type of cancer that affects the blood and bone marrow, and patients with leukemia are immunocompromised, making them more susceptible to infections and complications. The periapical abscess is a localized infection at the tip of a tooth root, which can be a common dental complication in patients with leukemia.

**Why the Correct Answer is Right**
In patients with leukemia, it is crucial to manage dental infections promptly to prevent further complications. The correct approach to treating a periapical abscess in a child patient with leukemia involves the use of antibiotics to control the infection, followed by dental extraction to remove the source of the infection. This is because patients with leukemia may have a compromised immune system, making them more susceptible to the spread of infection. The use of antibiotics is essential to prevent the spread of infection to other parts of the body.

**Why Each Wrong Option is Incorrect**
**Option A:** This option may involve only antibiotic therapy without dental extraction, which may not be sufficient to treat the periapical abscess in a patient with leukemia.
**Option B:** This option may involve only dental extraction without antibiotic therapy, which may lead to the spread of infection in a patient with a compromised immune system.
**Option C:** This option may involve a combination of antibiotic therapy and dental extraction, but it may not be the most appropriate approach in a child patient with leukemia.

**Clinical Pearl / High-Yield Fact**
In patients with leukemia, it is essential to manage dental infections promptly to prevent further complications. This includes the use of antibiotics to control the infection, followed by dental extraction to remove the source of the infection.

**Correct Answer:** C.