  A new approach to constructing coherent states (CS) and semiclassical states
(SS) in magnetic-solenoid field is proposed. The main idea is based on the fact
that the AB solenoid breaks the translational symmetry in the xy-plane, this
has a topological effect such that there appear two types of trajectories which
embrace and do not embrace the solenoid. Due to this fact, one has to construct
two different kinds of CS/SS, which correspond to such trajectories in the
semiclassical limit. Following this idea, we construct CS in two steps, first
the instantaneous CS (ICS) and the time dependent CS/SS as an evolution of the
ICS. The construction is realized for nonrelativistic and relativistic spinning
particles both in (2+1)- and (3+1)- dimensions and gives a non-trivial example
of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS
depending on their parameters (quantum numbers) describe both pure quantum and
semiclassical states. An analysis is represented that classifies parameters of
the CS in such respect. Such a classification is used for the semiclassical
decompositions of various physical quantities.
