  TXS 0506+056, a source of the extreme energy neutrino event, IceCube-170922A,
was observed on 22 September 2017. The Fermi-LAT detector reported high energy
(HE) $\gamma$-ray flare between 100 MeV and 100 GeV starting from 15 September
2017 from this source. Several attempts to trace the very high energy (VHE)
gamma-ray counterparts around the IceCube-170922A resulted in no success. Only
after 28 September, the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC)
telescopes observed the first VHE gamma-rays from the blazar above 100 GeV. The
$\sim$ 41 hr survey resulted in VHE-$\gamma$ ray activity till 31 October 2017.
Here we propose the extended GeV $\gamma-$rays can be explained by taking two
production channels, electron synchrotron self Compton and proton synchrotron
for HE and VHE emissions, respectively. The 45 days of VHE emission from the
peak of the HE-flare can be explained with $ {L_p'}{\simeq}10^{47}$ erg/sec in
the jet frame and magnetic field of 2.4 G, consistent with the ${L}_{Edd}$ for
a blackhole mass $5\times 10^{9} {M}_\odot$
