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In discussing non-commutative spacetime, the generally studied$\theta$-Poincare model is inconsistent with bound states. In this Letter, wedevelop the formalism and study the phenomenology of another model$\mathcal{B}_{\chi \hat{n}}$ by the twisted permutation algebra and extend thePauli Exclusion Principle(PEP) into non-commutative spacetime. The model alsoimplies time quantization and can avoid UV/IR mixing. Applying it to atomicsystems, we show that the model with newly induced phase factors can causeexotic transitions consisting of three electrons in the 1S orbit of atoms. Thetransition rate is derived, and the upper bound of non-commutative parameter$\chi$ is thus set by utilizing data from the low-energy and low-backgroundexperiments, where strongest constraint $\chi\leq4.05\times10^{-30}$ eV$^{-1}$at 90\% C.L. is given by XENONnT, with the time quanta $\Delta t\sim 2.67\times10^{-45} s$, equivalent to twenty times smaller than the Planck time.

Spherically Symmetric Noncommutative Spacetime via Exotic Atomic Transitions