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In this work we study braneworld configurations in the scalar-tensorrepresentation of the $f\left(R,T\right)$ gravity theory in the presence of aCuscuton term in the source field matter Lagrangian. We start by deriving thescalar-tensor representation of the theory and obtaining its respectiveequations of motion. We then introduce the standard metric for a flatbraneworld 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 obtainednumerically. In these cases, the Cuscuton term effectively amplifies theeffect, 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 $R+G\left(T\right)$, forwhich only the scalar fields $\varphi$ or $\psi$ are present, respectively, andwe prove that the presence of the scalar field $\varphi$ is essential in thedevelopment of internal structure on the brane.

Effects of Cuscuton dynamics on braneworld configurations in the scalar-tensor representation of $f\left(R,T\right)$ gravity