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Transverse Single Spin Asymmetries (TSSAs) in transversely polarizedproton-proton collisions ($p^{\uparrow}+p$) have been a fruitful source forstudying the spin structure of the proton. In the 2015 RHIC data takingperiods, collisions of polarized protons with nuclei ($p^{\uparrow}+A$) weremade for the first time. The measurements of TSSAs in $p^{\uparrow}+p$ and$p^{\uparrow}+A$ collisions can provide a unique opportunity to investigate theorigin of TSSA in a gluon-rich target nucleus and provide a tool to studynuclear effects in $p+A$ collisions. This presentation will report PHENIXresults of TSSAs for charged hadrons ($h^{\pm}$) at forward and backwardrapidity ($1.4<|\eta|<2.4$) over the transverse momentum ranges $1.25<p_{T}<7.0\mathrm{\ GeV}/c$ and Feynman-$x$ ranges ($-0.2<x_{F}<0.2$) from$p^{\uparrow}+p$, $p^{\uparrow}+\mathrm{Al}$, and $p^{\uparrow}+\mathrm{Au}$collisions at $\sqrt{s_{\rm NN}}= 200$ GeV.

Transverse Single Spin Asymmetries of charged hadrons at forward and  backward rapidity from $p^{\uparrow}+p$, $p^{\uparrow}+\mathrm{Al}$, and  $p^{\uparrow}+\mathrm{Au}$ collisions in PHENIX