  We elaborate on a novel superconformal mechanics model possessing
D(2,1;alpha) symmetry and involving extra U(2) spin variables. It is the
one-particle case of the N=4 superconformal matrix model recently proposed in
arXiv:0812.4276 [hep-th], and it generalizes to arbitrary alpha\neq0 the
OSp(4|2) superconformal mechanics of arXiv:0905.4951 [hep-th]. As in the latter
case, the U(2) spin variables are described by a Wess-Zumino action and define
the first Hopf map S^3 -> S^2 in the target space. Upon quantization, they
represent a fuzzy sphere. We find the classical and quantum generators of the
D(2,1;alpha) superalgebra and their realization on the physical states. The
super wavefunction encompasses various multiplets of the SU(2)_R and SU(2)_L
subgroups of D(2,1;alpha), with fixed isospins. The conformal potential is
determined by the external magnetic field in the Wess-Zumino term, whose
amplitude is quantized like in the OSp(4|2) case. As a byproduct, we reveal new
invariant subspaces in the enveloping algebra of D(2,1;alpha) for our quantum
realization.
