Protostellar outflows exhibit large variations in their structure depending on the observed gas emission. To understand the origin of the observed variations, it is important to analyze the differences in the observed morphology and kinematics of the different tracers. The James Webb Space Telescope (JWST) allows us to study the physical structure of the protostellar outflow through well-known near-infrared shock tracers in a manner unrivaled by other existing ground-based and space-based telescopes at these wavelengths. This study analyzes the atomic jet and molecular outflow in the Class I protostar, TMC1A, utilizing spatially resolved Fe II and H2 lines to characterize the morphology and to identify previously undetected spatial features, and compare them to existing observations of TMC1A and its outflows observed at other wavelengths. We identified a large number of Fe II and H2 lines within the G140H, G235H, and G395H gratings of the NIRSpec IFU observations. We analyzed their morphology and position-velocity (PV) diagrams. From the observed Fe II line ratios, the extinction toward the jet is estimated. We detected the bipolar Fe jet by revealing, for the first time, the presence of a redshifted atomic jet. Similarly, the redshifted component of the H2 slower wide-angle outflow was observed. The Fe II and H2 redhifted emission both exhibit significantly lower flux densities compared to their blueshifted counterparts. Additionally, we report the detection of a collimated high-velocity ($ 100$ km $), blueshifted H2 outflow, suggesting the presence of a molecular jet in addition to the well-known wider angle low-velocity structure. The Fe II and H2 jets show multiple intensity peaks along the jet axis, which may be associated with ongoing or recent outburst events. In addition to the variation in their intensities, the H2 wide-angle outflow exhibits a ring-like structure. The blueshifted H2 outflow also shows a left-right brightness asymmetry likely due to interactions with the surrounding ambient medium and molecular outflows. Using the Fe II line ratios, the extinction along the atomic jet is estimated to be between $A_ V $ = 10--30 on the blueshifted side, with a trend of decreasing extinction with distance from the protostar. A similar $A_ V $ is found for the redshifted side, supporting the argument for an intrinsic red-blue outflow lobe asymmetry rather than environmental effects such as extinction. This intrinsic difference revealed by the unprecedented sensitivity of JWST, suggests that younger outflows already exhibit the red-blue side asymmetry more commonly observed toward jets associated with Class II disks.
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