Given the triangular design of a three-core oppositely directed coupler, this work shows that it is possible to observe the modulational instability (MI) zones caused by the nonlinear saturation effect. Two channels in this design are built from a material with a low refractive index (Channel 1, 3), whereas one is built from a material with a high index (Channel 2). The governing coupled nonlinear Schrödinger equations are modified with the presence of saturable nonlinearity and coupling terms. In the presence of typical saturable nonlinearity, we are able to determine the dispersion relation for the optical coupler under investigation. Using a linear stability analysis, we look at the modulation instability characteristic gain in the normal and anomalous group-velocity dispersion regimes. We significantly increased the physical system parameter range to account for different eventualities. The analytical results demonstrate that new instability bands are created in system parameters anomalous and normal dispersion regimes, in contradiction to Shafeeque et al. (2016). MI can be managed using nonlinear and power factors. We present novel techniques for produce and control the MI in oppositely directed three-core couplers in the impacts of nonlinear saturation.