We report a series of numerical experiments for the propagation of a momentum pulse representing a chromospheric jet, simulated using an idealized magnetohydrodynamic model. The jet in a stratified lower solar atmosphere is subjected to a varied initial driver (amplitude, period) and magnetic field conditions to examine the parameter influence over jet morphology and kinematics. The simulated jet captured key observed spicule characteristics including maximum heights, field-aligned mass motions/trajectories, and cross-sectional width deformations. Next, the jet features also show a prominent bright, bulb-like apex, similar to reported observed chromospheric jets, formed due to the higher density of plasma and/or waves. Furthermore, the simulations highlight the presence of not yet observed internal crisscross/knots substructures generated by shock waves reflected within the jet structure. Therefore we suggest verifying these predicted fine-scale structures in highly localized lower solar atmospheric jets, e.g., in spicules or fibrils by high-resolution observations, offered by the Daniel K. Inoyue Solar Telescope or otherwise.