An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under the influence of a singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that the particle is transformed into a composite system which consists of quasiparticles, quasiholes, and magnetic fluxes. Such a system is endowed with generalized statistics determined by a grading group and a commutation factor on it. Composite systems corresponding to the quantum Hall effect and the electronic magnetotransport anomaly are described. The Fock space representation is also given.