corresponding field actions were constructed with the use of the unitary infinite-dimensional representations of $\overline{\rm SL(2,R)}$ [@tors]–[@pld]. Nevertheless, the problem of quantizing the theory is still open here. This is connected with the search for the most appropriate set of initial equations for subsequent constructing the action as a basic ingredient for quantization of the theory. Besides, there is a difficulty in quantization of such a theory related to the infinite-component nature of the fractional spin field which is used to describe in a covariant way one-dimensional irreducible representations of the (2+1)-dimensional quantum mechanical Poincaré group $\overline{\rm ISO(2,1)}$, specified by the values of mass and arbitrary (fixed) spin. Due to this fact, an infinite set of the corresponding Hamiltonian constraints must be present in the theory to exclude an infinite number of the ‘auxiliary’ field degrees of freedom and leave in the theory only one physical field degree of freedom. This infinite set of constraints should appropriately be taken into account. But, on the other hand, the infinite-component nature of the fractional spin field indicates the possible hidden nonlocal nature of the theory, and, therefore, can be considered in favour of existence of the anyonic spin-statistics relation [@fro1; @fro2] for 