  The non-Hermitian skin effect (NHSE) is a phenomenon where the bulk states
tend to the boundary within a non-Hermitian Hamiltonian system, with broad
applications across various fields. A comprehensive understanding of anomalies
in skin modes associated with NHSEs is essential for practical applications.
Recently, some innovative works reported the suppression and enhancement of
NHSEs through the application of magnetic fields, respectively. In our work, we
engineered onsite potential energy distribution and found non-monotonic and
monotonic suppression patterns on skin modes similar to magnetic fields. These
suppression patterns represent characteristic transitions as the onsite
potential distribution shifts from order to disorder. Relying only on onsite
potential energy engineering, we have not only deepened our insight into the
relationship and distinctions between order and disorder, but also developed a
general strategy to demonstrate both robustness and controllable adjustability
of the skin modes. By integrating with the scaling theory of disorder, we have
extended the concept of controllable suppression of NHSEs to higher-dimensional
systems.
