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We describe the family of supersymmetric twists of $\mathcal N = 4$ superYang--Mills theory using derived algebraic geometry, starting from holomorphicChern--Simons theory on $ \mathcal N = 4$ super twistor space. By consideringan ansatz for categorical geometric quantization of the family of furthertwists of a fixed holomorphic twist, we give a quantum field-theoreticsynthesis of the categories of twisted D-modules occuring in the quantumgeometric Langlands correspondence.

Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory