  We propose a novel way of modulating exceptional topology by implementing
Floquet engineering in non-hermitian (NH) systems. We introduce Floquet
exceptional topological insulator which results from shining light on a
conventional three-dimensional NH topological insulator. Lightmatter
interaction facilitates the quantum phases of matter to exhibit a novel
phenomenon, where, the point gaps in the bulk host surface states. These
distinct surface states either fill the point gap in the complex eigenspectrum
or exhibit exceptional points in the presence of a magnetic field. We also
highlight the existence of a quantum anomaly generated by photo-induced
modulation. The existence of the Floquet biorthogonal Chern number and spectral
winding number show that the momentum slices exhibit NH skin effect, even
though the system as a whole does not. We also employ wave-dynamics evolution
to illustrate the NH surface skin effect.
