  In this work we study braneworld models in generalized $f\left(R,T\right)$
gravity theories where the action depends on a function of the Ricci scalar $R$
and the trace of the stress-energy tensor $T$. We explore the so-called
scalar-tensor representation of the theory, where the dependence on $R$ and $T$
are exchanged for two auxiliary real scalar fields. We introduce a first-order
formalism to relate the auxiliary fields with the source field of brane and
analyze four distinct possibilities of current interest regarding
compactification and asymmetry of the brane. We investigate the behavior of the
auxiliary fields and their stability in each one of the four cases. For the
models where the solution of the source field engenders compact behavior, the
auxiliary fields exhibit a hybrid structure, behaving differently inside and
outside the compact region described by the source configuration. In
particular, we found that the solutions of the auxiliary fields are
significantly modified in models where the geometry is strongly influenced by
the source field. Moreover, for the model capable of engendering asymmetric
features, the two auxiliary fields also respond to modifications on the
parameter that controls the asymmetry of the system.
