The reconstruction of an inflationary universe considering the parametrization of the scalar spectral index as a function of the number of e - folds in the framework of a modified Friedmann equation is analyzed. In this context, we examine the possibility of reconstructing the Hubble parameter together with the effective potential considering a modified Friedmann equation specified by F(H)proportional to rho , where F(H) corresponds to an arbitrary function of the Hubble parameter H and rho denotes the energy density associated with the matter in the Universe. To reconstruct the background variables during the inflationary scenario, we develop a new methodology by expressing the spectral index in terms of the Hubble parameter and its derivatives. Thus, we derive a general formalism for the reconstruction of inflation, employing the slow-roll approximation in conjunction with the parametrization of the scalar spectral index as a function of the number of e-folds, N. As specific examples, we consider the simplest attractor ns - 1 = - 2/N together with different functions F(H) , associated to the modified Friedmann equation, to rebuild the Hubble parameter and the effective potential in terms of the scalar field phi. Additionally, we analyze the reheating epoch by assuming a constant equation of state parameter, determining the temperature and the number of e-folds during this period. This is done using the background variables obtained from the reconstruction of the various F(H) -models studied. In addition, we restrict several parameters related to the reconstructed inflationary models F(H)- during the inflation and reheating epochs, utilizing current astronomical data from Planck and BICEP/Keck results.