It is well known that the bandgap of 2D transition metal dichalcogenides (TMDs) in the quantum confinement regime increases with a decrease in the number of layers. In this work, we show the effect of lattice strain on the dependence of the gap. We have designed an ideal system in the form of common-cationic alloyed-TMDs, Mo(S_1−xSe_x)₂, for such studies. With a large difference between the ionic radii of the two chalcogens, the nanoflakes of the alloys possessed a lattice strain and have been found to yield a lower bandgap than those of both the end-members, MoS₂ and MoSe₂. More importantly, the dependence of the bandgap on the layer number in the nanoflakes of the alloys turned out to be steeper than in conventional binary TMDs. The experimental results imply that the lattice strain in 2D semiconductors has contributed to the effect of the quantum confinement phenomenon in addition to decreasing the bandgap, the latter being earlier predicted from a theoretical model. We have derived the electronic bandgap and the band-edge energies of the series of alloyed-TMDs in their nanoflake forms and the dependences on the number of layers from the density of states (DOS), as obtained from scanning tunneling spectroscopy (STS) recorded in a scanning tunneling microscope (STM) in an extremely localized manner.