  We study precursor states of fractional topological insulators (FTIs) in
interacting fermionic ladders with spin-orbit coupling. Within a
microscopically motivated bosonization approach, we investigate different
competing phases depending on same-spin and interspin interactions at
fractional effective filling $\nu=1/3$ per spin. In the spin-decoupled limit,
we find that strong repulsive interactions of already moderate range may lead
to a partially gapped state with two time-reversed copies of a quasi-one
dimensional Laughlin phase. This FTI precursor competes with an interleg
partially gapped phase displaying quasi long-range density wave order, however
it may be stabilized if interactions have suitable anisotropy, or are
sufficiently near SU($2$) symmetry, in leg space. When the FTI phase is
present, it is moderately robust to small interspin interactions; these
introduce competing partially gapped phases of orbital antiferromagnetic and
bond density wave character. Performing a strong coupling analysis of the FTI
precursor regime, we find that the main effect of interspin interactions is to
induce correlated quasiparticle backscattering between the precursor FTI edge
modes. Although this process competes with the topological phase, we show, by
considering an array of ladders, that its influence may disappear upon
approaching the two dimensional case. Considering time-reversal symmetry
breaking perturbations, we also describe a protocol that adiabatically pumps
$1/6$ charge per half-cycle, thus providing a quantized FTI signature arising
already in the single ladder regime.
