Different orientations of $alpha$-clustered carbon nuclei colliding with heavy ions can result in a large variation in the value of anisotropic flow. Thus, photon flow observables from clustered ${rm^{12}C}$ and ${rm^{197}Au}$ collisions could be a potential probe to study the `direct photon puzzle. We calculate the transverse momentum spectra and anisotropic flow coefficients ($v_n$) of thermal photons from collisions of triangular $alpha$-clustered carbon and gold at $sqrt{s_{rm NN}}=200$ GeV at RHIC using a hydrodynamic model framework and compare the results with those obtained from unclustered carbon and gold collisions. The slope of the thermal photon spectra is found to vary moderately for different orientations of collisions. However, we find that the elliptic ($v_2$) and triangular flow ($v_3$) coefficients of direct photons for specific configurations are significantly larger and predominantly formed by the QGP radiation. A strong anti-correlation between initial spatial ellipticity and triangularity is observed in an event-by-event framework of $alpha$-clustered ${rm C+Au}$ collisions. These special features provide us an opportunity to detect the exotic nature of cluster structure inside carbon nucleus using the photon probe in the future experiments.
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