  We study the spin transport through a 1D quantum Ising-XY-Ising spin link
that emulates a topological superconducting-normal-superconducting structure
via Jordan-Wigner (JW) transformation. We calculate, both analytically and
numerically, the spectrum of spin Andreev bound states and the resulting
$\mathbb{Z}_2$ fractional spin Josephson effect (JE) pertaining to the emerging
Majorana JW fermions. Deep in the topological regime, we identify an effective
time-reversal symmetry that leads to $\mathbb{Z}_4$ fractional spin JE in the
$\textit{presence}$ of interactions within the junction. Moreover, we uncover a
hidden inversion time-reversal symmetry that protects the $\mathbb{Z}_4$
periodicity in chains with an odd number of spins, even in the
$\textit{absence}$ of interactions. We also analyze the entanglement between
pairs of spins by evaluating the concurrence in the presence of spin current
and highlight the effects of the JW Majorana states. We propose to use a
microwave cavity setup for detecting the aforementioned JEs by dispersive
readout methods and show that, surprisingly, the $\mathbb{Z}_2$ periodicity is
immune to $\textit{any}$ local magnetic perturbations. Our results are relevant
for a plethora of spin systems, such as trapped ions, photonic lattices,
electron spins in quantum dots, or magnetic impurities on surfaces.
