In this study, we have constructed an extended version of Ginzburg-Landau theory of superconductivity starting from the exponential non-standard Lagrangian. An extended Ginzburg-Landau coherence length and an extended Ginzburg-Landau parameter emerge in the theory without affecting the Abrikosov's fluxoid quantization law. We have discussed the Abrikosov's periodic vortex lattice problem and we have observed that plausible solutions give rise to a shrink in the energy levels. We have also found that a transition between a type-II and a type-I superconductor takes place forκ=2/2whereas a transition between a new type-III and a type-I superconductor takes place for κ=ζ2/4 where ζ is a physical parameter. The new effective field of type III puts a supplementary limit for supercooling of the normal phase in superconductors. It was also revealed that a geometric transition from the square lattice to the rectangular lattice, a phenomenon which is detected in a number of superconductor's states.