<p>The linear and weakly nonlinear instability of triple-diffusive convection in a Darcy–Brinkman porous layer saturated with a Navier–Stokes–Voigt fluid is investigated analytically. The instability is driven by competing thermal and solutal buoyancy forces in the presence of viscoelastic stresses arising from a Voigt-type strain-rate regularization. Linear instability analysis reveals that the Kelvin–Voigt parameter plays a decisive role in oscillatory convection, exerting either stabilizing or destabilizing effects depending on the solute Darcy–Rayleigh number. A distinctive feature of the system is the emergence, under certain parametric conditions, of a disconnected closed oscillatory instability branch separate from the stationary one. In this regime, the neutral stability boundary is defined by three distinct thermal Darcy–Rayleigh numbers, in sharp contrast to the single threshold that characterizes the corresponding double-diffusive system. A weakly nonlinear stability analysis yields a cubic complex Landau amplitude equation governing the evolution of the disturbance amplitude, suggesting the possibility of subcritical bifurcations under certain parametric conditions. Heat and mass transport are quantified using time- and area-averaged Nusselt and Sherwood numbers, which increase with the Darcy–Prandtl number but decrease with increasing Darcy number and the effective heat capacity group, while variations in the Kelvin–Voigt parameter induce crossover behavior in the transport characteristics. These results clarify the subtle interplay between buoyancy, diffusion, and viscoelastic effects in regulating convection in triply diffusive porous media.</p>