  We explore the properties of the holographic fermions in extremal $R$-charged
black hole background with a running chemical potential, as well as the dipole
coupling between fermions and the gauge field in the bulk. We find that
although the running chemical potential effect the location of the Fermi
surface, it does not change the type of fermions. We also study the onset of
the Fermi gap and the gap effected by running chemical potential and the dipole
coupling. The spectral function in the limit $\omega\rightarrow0$ and the
existence of the Fermi liquid are also investigated. The running chemical
potential and the dipole coupling altogether can make a non-Fermi liquid become
the Landau-Fermi type.
