What is the lineage status of a child born to a married female slave resulting from illicit intercourse?

Primary text

If she gives birth, the child is not attributed to the man who committed the intercourse. Ahmad [Ibn Hanbal] stated that the child does not belong to the adulterer because she is within the established marital relation (*firash*) of another man, and thus her offspring does not join him, similar to an unrelated woman (*ajnabiyyah*).