  Long-range multi-particle correlations in heavy-ion collisions have shown
conclusive evidence of the hydrodynamic behavior of strongly interacting
matter, and are associated with the final-state azimuthal momentum anisotropy.
In small collision systems, azimuthal anisotropy can be influenced by the
hadronization mechanism and residual jet-like correlations. Thus, one of the
motives of the planned p--O and O--O collisions at the LHC and RHIC is to
understand the origin of small system collectivity. As the anisotropic flow
coefficients ($v_n$) are sensitive to the initial-state effects including
nuclear shape, deformation, and charge density profiles, studies involving
$^{12}$C and $^{16}$O nuclei are transpiring due to the presence of exotic
$\alpha$ ($^{4}$He) clusters in such nuclei. In this study, for the first time,
we investigate the effects of nuclear $\alpha$--clusters on the azimuthal
anisotropy of the final-state hadrons in p--C and p--O collisions at
$\sqrt{s_{\rm NN}}= 9.9$ TeV within a multi-phase transport model framework. We
report the transverse momentum ($p_{\rm T}$) and pseudorapidity ($\eta$)
spectra, participant eccentricity ($\epsilon_2$) and triangularity
($\epsilon_3$), and estimate the elliptic flow ($v_2$) and triangular flow
($v_3$) of the final-state hadrons using the two-particle cumulant method.
These results are compared with a model-independent Sum of Gaussians (SOG) type
nuclear density profile for $^{12}$C and $^{16}$O nuclei.
