Step 1: The word 'posthumous' literally means occurring after death, and in this legal context the relevant death is that of the father.
Step 2: A posthumous child is therefore one already conceived who is then born after the biological father has died.
Step 3: This carries inheritance and legitimacy implications, which is why the definition centers on the father.
Step 4: The scenarios involving the mother's death, both parents' death, or abandonment are distractors and do not describe a posthumous child.
\[\boxed{\text{Delivered after the death of the biological father}}\]