Inverse compton (IC) scattering of lower frequency photons by relativistic electronsrnwas used as a method for the production of high-energy gamma-rays in an accretingrnneutron stars. A spectrum function is derived.Based on which we obtained two newrnresults. First there is a maximum scattered photon energy for a given resonant scatteringrnwhich depends on both the incident electron energy and the magnetic field, butrnis independent of the incident photon energy. It is also found that the common upperrnlimit of the scattered photon energy is the highest scattered photon energy for anyrngiven incident photon and electron energy. Thus this may have physical implicationsrnfor Gamma-ray production