  The presence of $\alpha$-clustered structure in the light nuclei produces
different exotic shapes in nuclear structure studies at low energies. Recent
phenomenological studies suggest that collision of heavy nuclei with
$\alpha$-clustered carbon ($^{12}$C) at relativistic energies can lead to large
initial state anisotropies. This is expected to impact the final momentum
anisotropies of the produced particles significantly. The emission of
electromagnetic radiations is considered to be more sensitive to the initial
state compared to hadronic observables and thus photon observables are expected
to be affected by the initial clustered structure profoundly. In this work we
estimate the production and anisotropic flow of photons from most-central
collisions of triangular $\alpha$-clustered carbon and gold at $\sqrt{s_{\rm
NN}}=200$ GeV using an event-by-event hydrodynamic framework and compare the
results with those obtained from unclustered carbon and gold collisions. We
show that the thermal photon $v_3$ for most central collisions is significantly
large for the clustered case compared to the case with unclustered carbon,
whereas the elliptic flow parameter does not show much difference for the two
cases. In addition, the ratio of anisotropic flow coefficients is found to be a
potential observable to constrain the initial state produced in relativistic
heavy-ion collisions and also to know more about the $\alpha$-clustered
structure in carbon nucleus.
