  Using the density-matrix renormalization group, we determine the different
topological phases and low-energy excitations of a time-reversal invariant
topological superconducting (TRITOPS) wire with extended s-wave
superconductivity, Rashba spin-orbit coupling (SOC) and on-site repulsion $U$,
under an externally applied Zeeman field $J$. For the case in which $J$ is
perpendicular to the SOC, the model describes a chain of Shiba impurities on
top of a superconductor with extended superconductor pairing. We identify the
different topological phases of the model at temperature $T=0$, and in
particular study the stability of the TRITOPS phase against the Zeeman field
$J$ and the chemical potential $\mu$, for different values of $U$. In the case
where the magnetic field $J$ is perpendicular to the SOC axis, the pair of
Kramers-degenerate Majorana zero modes at the edges of the system that exist
for $J=0$, remain degenerate until a critical value of the magnetic field is
reached. For $J$ parallel to the SOC and up to moderate values of $U$, the
fractional spin projection $\langle S_y \rangle=1/4$ at the ends, found for
non-interacting wires at $U=0$, is recovered. In addition, the analytic
expression that relates $\langle S_y \rangle$ with $J$ for finite
non-interacting chains is shown to be universal up to moderate values of $U$.
