**Core Concept**
A posthumous child refers to a child born after the death of the father. This concept is relevant in forensic medicine, particularly in cases of paternity disputes or inheritance issues. The definition of a posthumous child is essential in understanding the legal and social implications of such births.

**Why the Correct Answer is Right**
The correct answer is **B. Child born after father's death** because the term "posthumous" specifically refers to events occurring after the death of a person. In this context, a posthumous child is one born after the father's demise, which can have significant consequences for inheritance, social security benefits, or other rights and responsibilities associated with the child. The father's death can also affect the child's paternity and rights to inheritance, making this definition crucial in forensic medicine.

**Why Each Wrong Option is Incorrect**
**Option A:** A stillborn child is one that is born dead or dies before or during birth, which does not necessarily relate to the father's death. Stillbirth can occur for various reasons, including maternal or fetal complications.

**Option C:** A child born after the mother's death is not a posthumous child, as the term specifically refers to the father's death. This option is incorrect because it misinterprets the definition of posthumous.

**Option D:** A fictitious child is a child whose existence is falsely claimed by a woman, which is unrelated to the concept of a posthumous child. This option is incorrect because it introduces a separate and unrelated concept in forensic medicine.

**Clinical Pearl / High-Yield Fact**
In forensic medicine, the definition of a posthumous child can have significant implications for inheritance, social security benefits, and paternity disputes. It is essential to understand this concept accurately to avoid misinterpreting the legal and social consequences of such births.

**✓ Correct Answer: B. Child born after father's death**