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Astrophysical very high energy (VHE) gamma-rays (with energies >30 GeV) are believed to result almost exclusively from the interactions of populations of highly relativistic particles with ambient matter or photon fields. The study of these VHE photons therefore allows us to examine the processes of particle acceleration in the Universe, and the extreme environments in which they occur. Gamma-rays are also highly directional, making them useful for studying the origin, acceleration, propagation, and composition of cosmic rays. This study uses the Monte Carlo method to simulate the process of extensive air showers being initiated when primary incident γ -rays with energies ranging from 10 GeV to 5 TeV interact with the atmosphere. The ultimate goal is to investigate and analyze the properties and lateral density distributions of Cherenkov light at different altitudes. The simulation considers various energies and zenith angles. The results show that a hump in the lateral density distribution of Cherenkov light is a distinctive feature of a γ -initiated shower, with the hump becoming less prominent at higher energy levels and altitudes. These significant findings not only facilitate better fitting of experimental data obtained from actual extensive air showers but also assist with estimating readings from detectors, thus advancing our understanding of these processes. [ABSTRACT FROM AUTHOR]