Аннотация:By the supersymmetrization of the simple algebraic technique proposed in [1] we obtain the complete classification of all basic (nonisomorphic) quantum deformations for the orthosymplectic Lie superalgebra osp(1|2;C) and its pseudoreal and real forms in terms of the classical r-matrices. In particular, we prove that pseudoreal compact form has only one quantum deformation (standart q-analog), and the D = 3, N = 1 Lorentz supersymmetry, which is the non-compact real form of osp(1|2;C), has four different Hopf-algebraic quantumdeformations: two standard q-analogs, and two (Jordanian and super-Jordanian) twist deformations. All basic Hopf-algebraic quantum deformations are presented in the explicit form.