Rotational misalignment or twisting of two monolayers of graphene strongly influences its electronic properties. Structurally, twisting leads to large periodic supercell structures, which in turn can support intriguing strongly correlated behavior. Here, we propose a highly tunable scheme to synthetically emulate twisted bilayer systems with ultracold atoms trapped in an optical lattice. In our scheme, neither a physical bilayer nor twist is directly realized. Instead, two synthetic layers are produced exploiting coherently coupled internal atomic states, and a supercell structure is generated via a spatially dependent Raman coupling. To illustrate this concept, we focus on a synthetic square bilayer lattice and show that it leads to tunable quasiflatbands and Dirac cone spectra under certain magic supercell periodicities. The appearance of these features are explained using a perturbative analysis. Our proposal can be implemented using available state-of-the-art experimental techniques, and opens the route toward the controlled study of strongly correlated flatband accompanied by hybridization physics akin to magic angle bilayer graphene in cold atom quantum simulators.