  The influence of a rotating magnetic field (in the $ab-$plane) on the density
of states has been investigated in the superconducting state of the nematic
FeSe superconductor using high sensitivity specific heat measurements. As
expected for (quasi-)nodal superconductors, oscillations in the specific heat
($C$) associated to the Doppler energy shift of Cooper pairs with momenta close
to the gap minima are observed. In the $T_c = 9$~K crystal, $C(\phi$) displays
a twofold symmetry at low temperature and low magnetic field confirming the
nematic character of FeSe from thermodynamical measurements. As expected, a
$\pi/2$ phase shift is observed for increasing temperatures (at $H=1$~T) but
the gap structure abruptly changes above $\sim 1$~K in this sample. At low
temperature, the maxima observed for $H||a-$axis at low $H$ split into lobes at
$\pm 45^\circ$ when the magnetic field is increased indicating an anomalous
field dependence of the gaps.
