We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates on the surfaces of GaAs/AlGaAs heterostructures. In the low mobility regime the classical Hall resistance line is proportional to the magnetic field as measured in the high temperature limit and cuts through the center of each Hall plateau. For high mobility samples we observe in linear response measurements that this symmetry is broken and the classical Hall line cuts the plateaus not at the center but higher B field edges of the plateaus. These experimental results confirm the unconventional predictions of a model for the quantum Hall effect taking into account mutual screening of charge carriers within the Hall bar. The theory is based on solving the Poisson and Schrödinger equations in a self-consistent manner.