  In this work we study braneworld configurations in the scalar-tensor
representation of the $f\left(R,T\right)$ gravity theory in the presence of a
Cuscuton term in the source field matter Lagrangian. We start by deriving the
scalar-tensor representation of the theory and obtaining its respective
equations of motion. We then introduce the standard metric for a flat
braneworld model with one extra dimension for the general case of a
$f\left(R,T\right)$ theory and study two different models for the source field.
Given the complexity of the field equations, these solutions are obtained
numerically. In these cases, the Cuscuton term effectively amplifies the
effect, by increasing the height of the stability potential barrier and,
consequently, the depth of the minimum of the graviton zero-mode on the brane.
Finally, we study the particular cases of $F(R)+T$ and $R+G\left(T\right)$, for
which only the scalar fields $\varphi$ or $\psi$ are present, respectively, and
we prove that the presence of the scalar field $\varphi$ is essential in the
development of internal structure on the brane.
