  We theoretically investigate the light scattering of the super- and
subradiant states which can be prepared by the excitation of a single photon
which carries an orbital angular momentum (OAM).\ With this helical phase
imprinted on the stacked ring of atomic arrays, the subradiant modes show
directional side scattering in the far-field, allowing for light collimation
and quantum storage of light with OAM.\ For the excitations with linear
polarizations, we find a discrete $C_4$ rotational symmetry in scattering for
the number of atoms $N$ $=$ $4n $ with integers $n$, while for circular
polarizations with arbitrary $N$, the azimuthal and $C_N$ symmetries emerge for
the super- and subradiant modes respectively.\ When the radial and azimuthal
polarizations are considered, a mode shift can happen in the scattering
pattern.\ The forward scattering of the superradiant modes can be enhanced as
we stack up the rings along the excitation direction, and for the subradiant
modes, we find the narrowing effects on the scattering in the azimuthal and the
polar angles when more concentric rings are added in the radial direction.\ By
designing the atomic spatial distributions and excitation polarizations,
helical-phase-imprinted subradiant states can tailor and modify the radiation
properties, which is detectable in the directional super- and subradiant
emissions and is potentially useful in quantum information manipulations.
