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For a Dynkin quiver $Q$ (of type ADE), we consider a central completion ofthe convolution algebra of the equivariant K-group of a certain Steinberg typegraded quiver variety. We observe that it is affine quasi-hereditary and provethat its category of finite-dimensional modules is identified with a block ofHernandez-Leclerc's monoidal category $\mathcal{C}_Q$ of modules over thequantum loop algebra $U_q(L\mathfrak{g})$ via Nakajima's homomorphism. As anapplication, we show that Kang-Kashiwara-Kim's generalized quantum affineSchur-Weyl duality functor gives an equivalence between the category offinite-dimensional modules over the quiver Hecke algebra associated with $Q$and Hernandez-Leclerc's category $\mathcal{C}_Q$, assuming the simpleness ofsome poles of normalized R-matrices for type E.

Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types