Bell nonlocality and entanglement in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>J</mml:mi> </mml:mrow> </mml:msub> </mml:math> decays into a baryon pa

We present a systematic analysis of Bell nonlocality and entanglement in $χ_{cJ}$($J=0,1,2$) decays into baryon pair($B\bar{B}$), with particular emphasis on their production via the process $e^+e^- \to ψ(2S) \to γχ_{cJ}$ at BESIII. From the baryon-antibaryon spin density matrix, we construct measurable Bell observables and concurrence, revealing a striking hierarchy of quantum correlations: $χ_{c0}$ decays exhibit maximal violation and entanglement; $χ_{c1}$ decays violate Bell inequalities for $θ_1 \in (0, π)$ with angle-modulated strength; we find that the $B\bar{B}$ pair in $χ_{c2}$ decays is in a separable state, and no indication of Bell inequality violation is observed. We provide complete analytical results for $J=0,1$ and quantitative, uncertainty-aware estimations for $J=2$ based on experimental inputs from BESIII. These results establish the $χ_{cJ}$ system produced via this radiative transition as a novel and promising platform for testing quantum entanglement and Bell nonlocality in high-energy collisions.