  We consider the external magnetic field effects on the two types of anyon
with fractional statistical parameters $p/q$ with coprimes $p$ and $q$, one
with fractional charge $e/q $ and flux $p \phi_0(=hc/e)$(type I), the other
with fractional flux $p \phi_0/q$ and fundamental charge $e$(type II). These
two-types of anyons show different behaviors in the presence of the external
magnetic field. We also considered the geometry in which a two-dimensional
plane contains an island of anyons with different statistical parameter in
their equilibrium. The equilibrium inside an island is shown to be periodic
with respect to the flux through the island. The period for the type I anyon
equals to the integer multiple of the fundamental flux quantum. In the case of
type II anyon the period is found to be the fractional multiple of the
fundamental flux quantum.
