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In this work, we investigate the time evolution of the pseudo-(R\'enyi)entropy after local primary operator quenches in 2D CFTs with $T\bar T/J\barT$-deformation. Using perturbation theory, we analyze the corrections to thesecond pseudo-R\'enyi entropy at the late time, which exhibit a universal form,while its early-time behavior is model-dependent. Moreover, we uncovernontrivial time-dependent effects arising from the first-order deformation ofthe $k^{\rm th}$ pseudo-R\'enyi entropy at the late time. Additionally, drawinginspiration from the gravitational side, specifically the gluing of two cutoffAdS geometries, we investigate the $k^{\rm th}$ pseudo-R\'enyi entropy forvacuum states characterized by distinct $T\bar{T}$-deformation parameters, aswell as for primary states acting on different deformed vacuum states. Ourfindings reveal additional corrections compared to the results ofpseudo-R\'enyi entropy for globally deformed vacuum states.

Pseudo entropy of primary operators in $T\bar{T}$/$J\bar{T}$-deformed CFTs