  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.
