The maximum energy possessed by an electron is when it is present:

As ${\mathrm{E}}_{\mathrm{n}}=-21.8\times {10}^{-19}\times \frac{{\mathrm{z}}^2}{{\mathrm{n}}^2}$
Thus; ${\mathrm{E}}_{\mathrm{n}}\propto \left(\frac{-1}{{\mathrm{n}}^2}\right)$where n is the number of orbit. Hence;
as the value of "n" increases, energy of the electron also increases; due to this reason; maximum energy is possessed by an electron when it is present at infinite distance from the nucleus.