  The Telescope Array (TA) experiment is located in the western desert of Utah,
USA, and observes ultra high energy cosmic rays (UHECRs) in the Northern
hemisphere. At the highest energies, $E>10$~EeV, the shape of cosmic ray energy
spectrum may carry an imprint of the source density distribution along the line
of sight different in different directions of the sky. In this study, we search
for such directional variations in the shape of the energy spectrum using
events observed with the Telescope Array's surface detector. We divide the TA
field of view into two nearly equal-exposure regions: the "on-source" region
which we define as $\pm 30^\circ$ of the supergalactic plane containing mostly
nearby structures, and the complementary "off-source" region where the sources
are further away on average. We compare the UHECR spectra in these regions by
fitting them to the broken power law and comparing the resulting parameters. We
find that the off-source spectrum has an earlier break at highest energies. The
chance probability to obtain such or larger difference in statistically
equivalent distributions is estimated as $6.2\pm1.1\times10^{-4}$ ($3.2\sigma$)
by a Monte-Carlo simulation. The observed difference in spectra is in a
reasonable quantitative agreement with a simplified model that assumes that the
UHECR sources trace the galaxy distribution from the 2MRS catalogue, primary
particles are protons and the magnetic deflections can be neglected.
