Here in, we have designed two new unfused non-fullerene small molecules based on asymmetric benzo[1,2-b:3.4-b', 6,5-b"]trithiophene (BTT) central donor core and different terminal units, i.e. 2-(3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile (NFA-4) and 1,3-diethyl-2-thioxodi hydropyrimidine-4,6(1H,5H)-dione (NFA-5) and their optical and electrochemical properties were investigated. Employing a wide band-gap copolymer D18, the binary D18: NFA-4 and D18:NFA-5 bulk heterojunction-based organic solar cells realized an overall power conversion efficiency of about 17.07% and 11.27 %, respectively. The higher value of power conversion efficiency for the NFA-4-based organic solar cells, as compared to the NFA-5 counterpart, is attributed to the enhanced values of short circuit current, open circuit voltage, and fill factor. After the incorporation of NFA-5 into the binary bulk heterojunction D18:NFA-4, the ternary organic solar cells attained a power conversion efficiency of 18.05 %, which is higher than that for the binary counterparts and attributed to the increased values of short circuit current, fill factor, and open circuit voltage. The increased value of short circuit current is associated with the effective utilization of excitons through the energy transfer from the NFA-5 to NFA-4 as the NFA-4 exhibits a more significant dipole moment than the NFA-5 and is effectively dissociated into a free charge carrier.