In this paper, we introduce a modified Fisher equation with two-unfolding parameters from the viewpoint of the field of singularity theory. The model is discussed under the Dirichlet and Neumann boundary conditions. We investigate the smoothness of the considered model and rigorously establish the unfolding parameters based on codimension using the restricted tangent space. The solution is obtained by Lyapunov Schmidt reduction and we subsequently perform bifurcation analysis of the proposed modified Fisher equation which yields pitchfork bifurcation.