  We scrutinize the behaviour of hydrogen atom's eigenvalues in a quantum
plasma as it interacts with electric field directed along $\theta=\pi$ and
exposed to linearly polarized intense laser field radiation. Using the
Kramers-Henneberger (KH) unitary transformation, which is semiclassical
counterpart of the Block-Nordsieck transformation in the quantized field
formalism, the squared vector potential that appears in the equation of motion
is eliminated and the resultant equation is expressed in KH frame. Within this
frame, the resulting potential and the corresponding wavefunction have been
expanded in Fourier series and using Ehlotzky's approximation, we obtain a
laser-dressed potential to simulate intense laser field. By fitting the
exponential-cosine-screened Coulomb potential into the laser-dressed potential,
and then expanding it in Taylor series up to $\mathcal{O}(r^4,\alpha_0^9)$, we
obtain the eigensolution (eigenvalues and wavefunction) of hydrogen atom in
laser-plasma encircled by electric field, within the framework of perturbation
theory formalism. Our numerical results show that for a weak external electric
field and gargantuan length of Debye screening parameter, the system is
strongly repulsive in contrast for strong external electric field and small
length of Debye screening parameter, the system is very attractive. This work
has potential application in the areas of atomic and molecular processes in
external fields including interactions with strong fields and short pulses.
