The “ancient and modern quarrel” in western literary criticism appears during

The correct option is Sixteenth century CE.

The "Querelle des Anciens et des Modernes" (Quarrel of the Ancients and the Moderns) was a major intellectual debate that erupted in European literary and cultural circles.
Although the debate reached its peak in the late 17th century (primarily in France and England), its origins and the initial friction between the authority of classical antiquity (the Ancients) and the achievements of contemporary writers (the Moderns) began taking shape during the Renaissance in the Sixteenth century CE (1500s).
During this period, the rediscovery of classical texts led to a critical evaluation of how modern vernacular literature and scientific thought compared to the ancient Greek and Roman traditions, laying the groundwork for the formal debate.