  Motivated by the order fractionalization in Kitaev-Kondo model, we propose an
exactly solvable spin-charge ladder model to study the order fractionalization
with discrete symmetry. The spin-charge ladder is composed of a spin chain and
a superconducting wire coupled via an Ising-type interaction, and we obtain the
exact solution in the flat band limit. The exact solution reveals the $Z_{2}$
order fractionalization with dual symmetry breaking and intertwined order
parameters. We investigate the topological phase transition of the spin-charge
ladder via the spectral chiral index, and identify the correlated topological
superconductor (TSC*) phase with gapped $Z_{2}$ Kondo flux excitations. We
demonstrate Majorana spinons generated odd frequency pairing in the
superconducting wire. We also discuss the order fractionalization in the
perspective of $Z_{2}$ lattice gauge theory.
