Adverbs make comparatives and superlatives with more and most. You'd say more quickly and most quickly.
more quickly, most quickly
More quickly is the comparative and Most quickly is the superlative.
The comparative is "more quickly" and the superlative is most quickly.
Quickly is an adverb The comparative form of quick is more quicker. The superlative form of quick is quickest.
Comparative form: Quicker Superlative form: Quickest
more quickly and most quickly
more quickly, most quickly
more quickly, most quickly
more quickly, most quickly
more quickly, most quickly
more quickly, most quickly
more quickly, most quickly
They are quicker and quickest, respectively.