  Motivated by the recent report of superconductivity in Fe-based ladder
materials, we study the pairing state of a multi-orbital t-J model defined on
two-leg ladders using the standard mean-field theory. We find that the
superconducting order parameters change sign between the $d_{xz}$ and $d_{yz}$
orbitals in most of the phase diagram. By analogy with the two-dimensional Fe
planes, we conclude that the leading pairing channel of this state belongs to
the $B_{1g}$ symmetry class, which is distinct from the common $s_{\pm}$ gap
with the $A_{1g}$ symmetry. By smoothly interpolating from planes into ladders,
we show that a first-order transition occurs between these two competing phases
when the dimension of the system is reduced.
