  In this work, we examine the main cosmological effects derived from a
time-varying coupling ($\bar{Q}$) between a dark matter (DM) fluid and a dark
energy (DE) fluid with time-varying DE equation state (EoS) parameter
($\omega_{DE}$), in two different coupled DE models. These scenarios were built
in terms of Chebyschev polynomials. Our results show that such models within
dark sector can suffer an instability in their perturbations at early times and
a slight departure on the amplitude of the cosmic structure growth
($f\sigma_{8}$) from the standard background evolution of the matter. These
effects depend on the form of both $\bar{Q}$ and $\omega_{DE}$. Here, we also
perform a combined statistical analysis using current data to put tighter
constraints on the parameters space. Finally, we use some selections criteria
to distinguish our models.
