  We construct a three-dimensional superconformal quantum mechanics (and its
associated de Alfaro-Fubini-Furlan deformed oscillator) possessing an $sl(2|1)$
dynamical symmetry. At a coupling parameter $\beta\neq 0$ the Hamiltonian
contains a $\frac{1}{r^2}$ potential and a spin-orbit (hence, a first-order
differential operator) interacting term. At $\beta=0$ four copies of undeformed
three-dimensional oscillators are recovered. The Hamiltonian gets diagonalized
in each sector of total $j$ and orbital $l$ angular momentum (the spin of the
system is $\frac{1}{2}$). The Hilbert space of the deformed oscillator is given
by a direct sum of $sl(2|1)$ lowest weight representations. The selection of
the admissible Hilbert spaces at given values of the coupling constant $\beta$
is discussed. The spectrum of the model is computed. The vacuum energy (as a
function of $\beta$) consists of a recursive zigzag pattern. The degeneracy of
the energy eigenvalues grows linearly up to $E\sim \beta$ (in proper units) and
quadratically for $E>\beta$. The orthonormal energy eigenstates are expressed
in terms of the associated Laguerre polynomials and the spin spherical
harmonics. The dimensional reduction of the model to $d=2$ produces two copies
(for $\beta$ and $-\beta$, respectively) of the two-dimensional $sl(2|1)$
deformed oscillator. The dimensional reduction to $d=1$ produces the
one-dimensional $D(2,1;\alpha)$ deformed oscillator, with $\alpha$ determined
by $\beta$.
