Studies of dielectric, optical and ferroelectric characteristics of trivalent Bi/Sm-modified barium titanate complex perovskite of a composition Bi0.5Ba0.5Sm0.5Ti0.5O3 (BBSTO), synthesized by adopting a mixed oxide (solid state) reaction technique, have been reported here. A single-phase tetragonal (space group P4mm) symmetry of BBSTO, after the evaluation of X-ray diffraction (XRD) data and pattern by Rietveld refinement, has been proposed. The microstructural analysis of pellet sample of BBSTO, carried out by field emission scanning electron microscope (FE-SEM), has shown uniform distribution and compactness of grains of varying size. Analysis of Fourier transform infrared spectrum of the material has provided the stretching vibration of Ba-Ti-O and O-Ti-O bonds, BiO6 (octahedral) as well as the bending vibration of Ti-O in octahedral [TiO6](2-) of BaTiO3. The UV-visible absorption spectra of the material have been used to evaluate the optical band gap of 1.78 and 1.56 eV for the direct and indirect allowed transition, respectively. The analysis of dielectric and electrical data, obtained in a wide range of temperature (25-500 degrees C) at different frequency (1 kHz-1000 kHz), exhibits various characteristics including dielectric relaxation and a ferroelectric phase transition. The mixed temperature coefficient of resistance (TCR) behavior, both negative-TCR and positive-TCR is observed in the BBSTO perovskite. The conduction mechanism of the material was studied with the help of the Jonscher's power law. The conduction mechanism was also found to follow the correlated barrier hopping (CBH) model. The logJ versus logE plots were analyzed to understand the leakage current behavior of the material with the help the SCLC (space charge-limited conduction) mechanism and Schottky mechanism.