In the field of optoelectronics, quantum dots (QDs) have gained interest due to easy modifications of electronics properties. Subsequently, the importance of nonlinear optical (NLO) properties is increasing day by day. In this work, we have systematically analyzed the NLO properties of phagraphene QDs with different shapes and sizes, employing density functional theory (DFT). Negative value of cohesive energy and absence of imaginary modes in the Raman spectra confirm the energetical stability of the QDs. Successful experimental realization of phagraphene nanoribbon have triggered the possibility of experimental feasibility of the QDs. Additionally, most of the QDs showcase high absorption in the UV region. 
Particularly, the variation of electronic bandgap and the number of delocalized $\pi$ electrons in the structure control the NLO responses of materials. Surprisingly, electronic bandgap as well as the number of $\pi$ electrons in the system can be easily tuned by varying the shapes and sizes of the phagraphene QDs. Both static and dynamical variations of polarizability $<\alpha>$, first-order $<\beta>$ and second-order hyperpolarizability $<\gamma>$ are calculated here. Maximum value of $<\alpha>$, $<\beta>$ and $<\gamma>$ are observed for different QDs. The variation of NLO responses with perturbing electric field leads to feasibility of applications in optoelectronics.