We consider the external magnetic field effects on the two types of anyons with fractional statistical parameter p/q with coprimes p and q, one with a fractional charge e/q and the other with a fractional flux p#PHI#_0/q by exact ground state wave function. We also study the geometry in which a two-dimensional strip of anyons contains an island of anyons with different statistical parameters in their equilibrium. The equilibrium inside an island is shown to be periodic with respect to the magnetic flux through the island. The period for the fractional charge anyon equals to the integer multiple of the fundamental flux quantum. On the other hand, in the case of the fractional flux anyon, the period is found to be the fractional multiple of the fundamental flux quantum.
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