Much effort has been put forth to develop unnatural, stable, hydrophobic base pairs with orthogonal recognition properties and study their effect on DNA duplex stabilisation. Our continuous efforts on the design of fluorescent unnatural biomolecular building blocks lead us to the synthesis of some triazolyl donor/acceptor unnatural nucleosides via an azide–alkyne 1,3-dipolar cycloaddition reaction as a key step, which we want to report herein. We have studied their photophysical properties and found interesting solvatochromic fluorescence for two of the nucleosides. Photophysical interactions among two donor–acceptor β-nucleosides as well as a pair of α/β-nucleosides have also been evaluated. Furthermore, we have exploited one of the fluorescent nucleosides in studying its interaction with BSA with the help of UV-visible and steady state fluorescence techniques. Our design concept is based on the hypothesis that a pair of such donor/acceptor nucleosides might be involved in π-stacking as well as in photophysical interactions, leading to stabilization of the DNA duplex if such nucleosides can be incorporated into short oligonucleotide sequences. Therefore, the designed bases may find application in biophysical studies in the context of DNA.