Optical and electronic properties of graphene quantum dots (GQDs) could be modified either by introducing heteroatoms on their surface or by covalently linking these with certain groups. In this work, time-dependent density functional theory (TD-DFT) with functional B3LYP/6-31G* has been used to study the effects of boron doping and surface-modified configurations of GQDs on the HOMO-LUMO gap and absorption spectra. The photoluminescence properties and quantum yield of GQDs have also been explored. Doping as well as a surface modification with boron configurations resulted in a decrease in the band gap and a red shift in absorption and photoluminescence/fluorescence spectra. As compared to surface modified GQDs, the presence of B atom in the edge modified GQDs has a pronounced effect on the tuning of the energy bandgap. Also, BCO2 is found to affect the electrical structures of GQDs more significantly as compared to BC2O. The fluorescence of surface-modified GQD is found fall in the near-infrared region with a quantum yield of 29 % rendering them suitable for bio-imaging applications. The results thus obtained are in good consonance with those reported in the literature.