  We consider the magnetic monopole in the axionic dark matter environment
(axionic dyon) in the framework of the Reissner - Nordstr\"om - de Sitter
model. Our aim is to study the distribution of the pseudoscalar (axion) and
electric fields near the so-called folds, which are characterized by the
profiles with the central minimum, the barrier on the left, and the maximum on
the right of this minimum. The electric field in the fold-like zones is shown
to change the sign twice, i.e., the electric structure of the near zone of the
axionic dyon contains the domain similar to a double electric layer. We have
shown that the described fold-like structures in the profile of the
gravitational potential, and in the profiles of the electric and axion fields
can exist, when the value of the dyon mass belongs to the interval enclosed
between two critical masses, which depend on the cosmological constant.
