<p>Particle accelerators play a key role in producing high-energy charged particle beams with applications in fundamental research, medicine, nuclear science, astrophysics, and industrial environments. The study of electron beam dynamics in a small-scale S-band (standing-wave) RF photoinjector with a 1.8-cell cavity is critical in monitoring the accurate emission, acceleration, and stability of the beam in the design stage. The findings from these experiments are directly relevant to radio and satellite (GPS, weather monitoring, deep space) communications, Wi-Fi (2.4 GHz), Bluetooth, and microwave (with optimal electrons received from radio) systems on which performance, signal strength, and system efficiency may be improved. Analysis of the effects of the RF electric field amplitude and initial phase on beam extraction and beam power gain were done by performing analytical modeling guided by calculations in MATLAB and Python. Magnesium material was found to be the best cathode material and allowed electron emission at lower fields compared to copper or lead. Maximum electron kinetic energy was approximately 4 MeV under optimal phase and field with peak electric field 100 MV/m with minimum phase slippage and high beam stability. These results offer practical guidelines to optimize compact photoinjector performance while revealing valuable information about electron beam responses on RF accelerator structures.</p>