Wave propagation in periodic media is crucial for energy transmission, enabling control over energy direction and isolation. This involves breaking the inversion symmetry of a spring-mass chain by introducing mirrored copies of periodic combinations, creating a unique, irreversible structure with distinct dispersion properties. The customizability and linearity of the interface lattice present the main challenge in controlling the interface mode. Our study focuses on designing a controllable on-demand interface mode using shape memory alloy-based smart material actuation mechanism. We included shape memory alloy-type springs along with the conventional springs in the analysis. SMA has the unique ability to change its phase in response to a temperature change due to the phase transition between martensite and austenite crystal structures. As a result, the modulus of elasticity also varies resulting in a change in stiffness. Through this system, the voltage-dependent stiffness can be tuned. This, in turn, enables the existence of an interface mode to be adjusted to the desired frequency and amplitude. The proposed system also allows us to obtain a range of split bandgaps that are dependent on controlling parameters. It is observed that the variation in the actuation voltage is to be controlled for the interface mode tuning and adjust stiffness accordingly. A generalized theoretical scheme is developed for several types of spring combinations at the interface and its effects are compared. Such system can significantly change the wave propagation in periodic media, leading to advancements in energy transmission systems with enhanced efficiency and versatility. Thus, the obtained interface mode within the bandgap can be tuned by the applied voltage enabling future application in wave focusing, wave guiding, and energy harvesting.