Solve this by matching the defining circumstance to the precise legal-medical vocabulary.
The defining circumstance: The child entered the world only after the father had already died, and laboratory DNA fingerprinting proved that the deceased man was genuinely the biological father. The single word for 'a child born after the death of its father' is posthumous - the prefix tells you it is an event occurring after death.
Legitimacy angle: A posthumous child is treated as legitimate if born within the accepted maximum period of gestation reckoned from the father's death, and confirmed paternity (as the DNA test provides here) cements that status and the child's inheritance rights.
Contrast the other terms:
- A suppositious child is one fraudulently substituted at birth and falsely claimed to be born of a particular woman, usually to grab property; the DNA proof of real parentage directly contradicts this.
- An illegitimate child is born of parents not married to each other - the stem gives no hint of that, and verified paternity points the other way.
Time-limit nuance: The legitimacy of a posthumous child hinges on the gestational interval from the father's death - a child born within the accepted maximum gestation period (commonly taken as about 280 days, extendable in disputed cases) is presumed his; one born well beyond that window raises a presumption against paternity, which is exactly why corroborative DNA fingerprinting is so valuable in such disputes.
Note on the options: Choices A and D both read 'Posthumous child', and the key marks A; the underlying answer is unambiguous.
$Answer = A\,(Posthumous\ child)$