  The $XYZ$ antiferromagnetic spin-$1/2$ chain with alternation of the exchange
and anisotropy couplings in the presence of uniform and staggered axial
magnetic fields is studied. The analysis is done using the effective quadratic
fermionic Hamiltonian resulting from the Hartee-Fock approximation. Combining
the exact and the mean-field methods, the local and string order parameters on
the ground-state phase diagram of the model are identified and calculated. We
found a topological phase with oscillating string order with a period of four
lattice spacings, not reported before for this model. A detailed analysis of
patterns of the string order is given. The special $XXZ$ limit of the model
with additional $U(1)$ symmetry brings about, in agreement with the
Lieb-Schultz-Mattis theorem and its extensions, plateaux of magnetization and
some additional conserving quantities. We have shown that in the $XYZ$ chain,
where the plateaux are smeared, the robust oscillating string order parameter
is continuously connected to its $XXZ$ limit. Also, the non-trivial winding
number and zero-energy localized Majorana edge states, as additional attributes
of topological order, are robust in that phase, even off the line of $U(1)$
symmetry.
