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This study explores the generation of electrostatic (ES) electron Kelvin–Helmholtz instability (EKHI) in collisionless plasma with a step-function electron velocity shear akin to that developed in the electron diffusion region in magnetic reconnection. In incompressible plasma, ES EKHI does not arise in any velocity shear profile due to the decoupling of the electric potential from the electron momentum equation. Instead, a fluid-like Kelvin–Helmholtz instability (KHI) can arise. However, in compressible plasma, the compressibility couples the electric potential with the electron dynamics, leading to the emergence of a new ES mode EKHI on Debye length λDe, accompanied by the co-generation of an electron acoustic-like wave. The minimum threshold of ES EKHI is ΔU>2cse, i.e., the electron velocity shear is larger than twice the electron acoustic speed cse. The corresponding growth rate is Im(ω)=((ΔU/cse)2−4)1/2ωpe, where ωpe is the electron plasma frequency.