is the purpose of the present paper to consider the Schwinger process of pair creation in the electrosphere of the quark stars, by systematically taking into account the main physical characteristics of the environment in which pair production takes place. The electric field in the electrosphere is not a constant, as assumed in the Schwinger model, but it is a rapidly decreasing function of the distance $z$ from the quark star surface. Therefore, in order to realistically describe the pair production process one must consider electron-positron creation in an inhomogeneous electric field. To study the pair production process we adopt the tunnelling approach and the fermion production rate in the electric field of the electrosphere is derived. The production rate is a local quantity, it depends on the distance to the quark star’s surface and it is a rapidly decreasing function of $z$. The emissivity and energy flux due to pair creation at the quark star surface is also considered. An important factor which can reduce significantly the pair production rate is the presence of a boundary (the quark star surface). For electric fields perpendicular to the boundary there is a significant reduction in the magnitude of the pair production 