Step 1: Read the key fact. The decisive detail is that the child was born after the death of his father, and DNA fingerprinting confirmed the dead man was indeed the biological father. We must give the medico-legal term for a child born after the father's death.
Step 2: Define the correct term. A posthumous child is a child born after the death of its father. ('Posthumous' literally means 'after death/burial'.) Such a child is legitimate provided it is born within the normal period of gestation after the father's death - the law recognises a maximum 'posthumous' gestation window (up to about 280-300+ days, and in some jurisdictions a child born within ~280 days of the husband's death is presumed legitimate). DNA confirmation of paternity, as here, settles the disputed paternity. Hence the child is a posthumous child.
Step 3: Why the other options are wrong.
(B) A suppositious child is a supposititious/fraudulently substituted child - a child falsely presented as having been born to a woman who did not actually give birth to it (baby substitution to claim inheritance/legitimacy). DNA fingerprinting confirming true biological parentage rules this out.
(C) An illegitimate child is one born to parents not lawfully married to each other; nothing in the stem indicates the parents were unmarried, and confirmed paternity of a child conceived during the father's lifetime supports legitimacy.
Step 4: About the duplicated option. Options A and D are both worded 'Posthumous child'; the printed answer key is A. The correct concept either way is posthumous child.
Final answer: A - Posthumous child.