Extremely High Synchrotron Peak (EHSP) blazars are observed to form a
small population of sources with high energy hump peaking at TeV
energies in their broad-band spectral energy distributions. The observed gamma-ray emission from these sources at GeV-TeV energies is described by unusual hard spectral indices. The observed spectral and temporal characteristics of these sources challenge the standard leptonic models for the broad-band emissions from blazars. Therefore, such sources provide astrophysical sites to investigate directly the particle acceleration, cooling of relativistic particles and indirectly probe the cosmological quantities like extragalactic background light (EBL) and intergalactic magnetic field (IMF) in the Universe. In this study, we investigate the spectral properties of the gamma-ray emission from EHSP blazars using observations from the Fermi-LAT catalogues (3FGL and 3FHL) along with the TeV observations using ground based telescopes. The observed TeV gamma-ray spectra are corrected for the EBL absorption using the most recent and updated EBL models to determine the intrinsic spectrum at the source. The intrinsic TeV spectra are combined with the MeV-GeV observations from the Fermi-LAT to study the gamma-ray emission from EHSP blazars in the broad energy band. The intrinsic gamma-ray spectra are then used to estimate the position of high energy peak in the spectral energy distribution. We also present the qualitative description for the observed spectral properties of EHSP blazars using different physical scenarios and discuss their importance for the upcoming CTA observatory.