Final answer:
The minarets of the Hagia Sophia serve no structural purpose, being added to the building as towers for the call to prayer.
Step-by-step explanation:
The architectural detail of the Hagia Sophia that serves no structural purpose is B. Minarets. The Hagia Sophia has four tall minarets, which were added around a thousand years after the building was initially constructed. Unlike the dome, pendentives, and buttresses that support the structure of the building, minarets were designed as towers from where the Muslim call to prayer is announced. This function is not related to the structural integrity of the building but rather serves a religious and cultural purpose.