States excited by the $^{99}\mathrm{Ru}(\ensuremath{\alpha},2n\ensuremath{\gamma})^{101}\mathrm{Pd}$, $^{88}\mathrm{Sr}(^{16}\mathrm{O},3n\ensuremath{\gamma})^{101}\mathrm{Pd}$, and $^{92}\mathrm{Zr}(^{12}\mathrm{C},3n\ensuremath{\gamma})^{101}\mathrm{Pd}$ reactions have been studied by measuring the $\ensuremath{\gamma}$-ray yield as a function of incident projectile energy, $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences, $\ensuremath{\gamma}$-ray angular distributions, and $\ensuremath{\gamma}$-ray linear polarizations. Three intense $\ensuremath{\gamma}$-ray cascades were observed. These cascades are produced by quasirotational bands built on the 5/${2}^{+}$, 7/${2}^{+}$, and 11/${2}^{\ensuremath{-}}$ intrinsic states of the nucleus. A decay scheme is given which includes states with energy up to 6488 keV and angular momentum up to 35/2. The quasirotational bands seen in $^{101}\mathrm{Pd}$ are similar to the bands in the adjacent even-even nuclei which suggests that this odd-$A$ nucleus can be described as a particle decoupled from an even-even core. A cascade of seven $\ensuremath{\gamma}$ rays in $^{102}\mathrm{Rh}$ was also observed following the $^{92}\mathrm{Zr}(^{12}\mathrm{C},p n)^{102}\mathrm{Rh}$ reaction.[NUCLEAR REACTION $^{99}\mathrm{Ru}(\ensuremath{\alpha},2n\ensuremath{\gamma})$, $E=16\ensuremath{-}24$ MeV; $^{92}\mathrm{Zr}(^{12}\mathrm{C},3n\ensuremath{\gamma})$, $E=45\ensuremath{-}56$ MeV; $^{88}\mathrm{Sr}(^{16}\mathrm{O},3n\ensuremath{\gamma})$, $E=56\ensuremath{-}64$ MeV; measured $\ensuremath{\sigma}(E)\ensuremath{\gamma}$, $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coin, $\ensuremath{\sigma}(\ensuremath{\theta})\ensuremath{\gamma}$, linear $P$; deduced decay scheme, $J$, $\ensuremath{\pi}$.]