  We study the \emph{orbital effects} of the synthetic magnetic fields in an
interacting square lattice two-leg fermionic ladder model with the
number-conserving pair hopping that hosting the Majorana bound states. By
utilizing density matrix renormalization group and exact diagonalization, we
identify a novel type-II topological Meissner $($\emph{topo}-Meissner$)$ phase
$($as distinguished from the low-field type-I \emph{topo}-Meissner state$)$
when threading a \emph{high} magnetic flux through the plaquette of the ladder,
which not only exhibits a large uniformly circulating chiral current along the
legs, the characteristics of the celebrated Meissner state, but also
accommodates a topologically protected ground-state manifold due to the
\emph{reentrant} emergence of the Majorana end modes. Our work reveals some
interesting interference effects resulting from the interplay between the gauge
fields and the strong interactions in establishing the intrinsic topological
states of matter in low-dimensional quantum systems.
