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, t…