The lead-free 0.94(Bi0.5Na0.5)TiO3-0.06BaTiO3 (BNT-6BT) at the morphotropic phase boundary (MPB) exhibits exceptional dielectric constant, polarization, and energy storage properties due to its unique arrangement of structural phases and instabilities. In this work, ferromagnetism is introduced into the ferroelectric BNT-6BT matrix by making 0–3 composites with Co0.65Zn0.35Fe2O4 (CZF), i.e., (1-x) BNT-6BT/x CZF, (x = 0.0, 0.25, 0.50, and 0.75). The structural dielectric, energy storage, and magnetic properties of these composites are studied under an Air and Nitrogen (N2) annealing atmosphere. The structural investigation indicates that the pristine BNT-6BT exhibits the coexistence of tetragonal ( P 4 b m ) and rhombohedral ( R 3 c ) phases. In contrast, all the BNT-6BT/CZF composite samples reveal the presence of cubic ( F d 3 ¯ m) phase alongside the tetragonal ( P 4 b m ), and rhombohedral ( R 3 c ) phases. In contrast to the Air-annealed BNT-6BT sample, N2-annealed samples were found to yield a ferroelectric-relaxor crossover followed by a higher dielectric constant (~ 2045), lower tangent loss (~ 0.07), higher polarization maximum (~ 12.31 µC/cm2), higher recoverable energy density (~ 201 mJ/cm3), and higher storage efficiency (~ 99%). Interestingly, N2 annealing induces exotic room-temperature ferromagnetism in non-magnetic BNT-6BT samples. Furthermore, the increase in the CZF doping not only eliminates the depolarization effect but also leads to an increase in dielectric constant (as high as 3919) and saturation magnetization (~ 58 emu/gm). Nonetheless, all the N2 annealing results in enhancement in dielectric constant, lowering of dielectric loss, and increase in Wrec, η, and saturation magnetization as compared to the Air-annealed counterparts. The superior physical properties of N2-annealed samples are ascribed to a substantial increase in the grain and grain boundary barrier properties under N2 annealing. [ABSTRACT FROM AUTHOR]