  In this letter, we present a novel exact scalar quasibound states solutions
in the extremal Reissner-Norstr\"om black hole background. We start with the
construction of the governing covariant relativistic scalar field equation, the
Klein-Gordon equation in the extremal Reissner-Norstr\"om black hole background
and applying the separation of variables anzat. The exact relativistic scalar
wave's angular solution is found in terms of the spherical harmonics while the
two independent radial wave solutions are, for the first time, exactly found
and presented in terms of the double confluent Heun functions. The solutions
are settled in the gravitational potential well and behave like an ingoing
waves approaching black hole's horizon, vanishing when approaching infinity.
The gravitationally bounded charged massive scalar fields are found to have
quantized complex valued energy levels while imaginary energy levels are
obtained for the charged massless scalar field, of both cases, indicating
decaying states. Further investigation shows that the extreme
Reissner-Nordst\"om black hole does not support scalar cloud. And with the help
of the obtained exact radial solutions, the Hawking radiation of the extremal
Reissner-Nordst\"om black hole is investigated and we find the zero temperature
of the black hole's horizon.
