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Understanding the spin structure of the proton is of large interest to thenuclear physics community and it is one of the main goals of the spin physicsprogram at the Relativistic Heavy Ion Collider (RHIC). Measurements from datataken by the PHENIX detector with transverse ($p^{\uparrow} + p$,$p^{\uparrow}$ + Al, $p^{\uparrow}$ + Au) proton polarization play an importantrole in this, in particular, due to the leading order access to gluons inpolarized protons. Transverse single-spin asymmetries (TSSAs) provide insightinto initial and final state spin-momentum and spin-spin parton-hadroncorrelations. In addition to possible final state contributions, $\pi^{0}$ and$\eta$ TSSAs access both quark and gluon correlations in the polarized proton.Furthermore, the $p^{\uparrow} + A$ data from RHIC provides an opportunity tostudy the effect of TSSAs in the presence of additional nuclear matter.Midrapidity $\pi^{0}$ and $\eta$ mesons are measured at PHENIX by detecting the2$\gamma$ decay with the electromagnetic calorimeter (EMCal) in the central armspectrometer, which has fine granularity for the resolution of separate decayphotons. New results for TSSAs of midrapidity $\pi^{0}$ and $\eta$ mesons in$\sqrt{s_{NN}} = 200$ GeV $p^{\uparrow}$ + Au and $p^{\uparrow}$ + Alcollisions from the 2015 running year will be presented, and compared with therecent $\sqrt{s} = 200$ GeV $p^{\uparrow} + p$ results.

Transverse Single-Spin Asymmetries of Midrapidity $\pi^{0}$ and $\eta$  Mesons in $\sqrt{s_{NN}} = 200$ GeV $p^{\uparrow}+$Au and $p^{\uparrow}+$Al  Collisions from PHENIX