A spectacular phenomenon that can occur in strongly correlated low dimensional systems is that of fractionalization. In such electronic systems, quasiparticles excitations can carry a fraction of the electron’s charge and can have anyonic quantum statistics which is neither fermionic nor bosonic. Here, mesoscopic ring geometries are introduced as a means of bringing out novel signatures of both charge fractionalization and non-Abelian anyonic statistics. It is shown that power maps of quasiparticle motion around a thin ring can act as measures of fractionalization complementary to recent cutting-edge studies in etched quantum wires. A proposal is presented for probing the non-Abelian statistics of recent tour de force realizations of fractional vortices in superconducting mesoscopic rings.