Summary: The first quantized theory of \(N= 2\), \(D= 3\) massive superparticles with arbitrary fixed central charge and (half) integer or fractional superspin is constructed. The quantum states are realized on the fields carrying a finite-dimensional, or a unitary infinite-dimensional, representation of the supergroups \(\text{OSp} (2|2)\) or \(\text{SU} (1, 1|2)\). The construction originates from quantization of a classical model of the superparticle we suggest. The physical phase space of the classical superparticle is embedded in a symplectic superspace \(T^* (R^{1,2})\times {\mathcal L}^{1|2}\), where the inner Kähler supermanifold \({\mathcal L}^{1|2}\cong \text{OSp} (2|2)/[\text{U} (1)\times \text{U} (1)]\cong \text{SU} (1,1|2)/[\text{U} (2|2)\times U(1)]\) provides the particle with superspin degrees of freedom. We find the relationship between Hamiltonian generators of the global Poincaré supersymmetry and the “internal” \(\text{SU} (1,1|2)\) one. Quantization of the superparticle combines the Berezin quantization on \({\mathcal L}^{1|2}\) and the conventional Dirac quantization with respect to spacetime degrees of freedom. Surprisingly, to retain the supersymmetry, quantum corrections are required for the classical \(N=2\) supercharges as compared to the conventional Berezin method. These corrections are derived and the Berezin correspondence principle for \({\mathcal L}^{1|2}\) underlying their origin is verified.