In photo-electric effect Einstein said that photons incidents on material and gives their energy which will gives kinetic energy to electrons. But i also want to know that why Compton's effect not works in this situation. In my view when photon incident on material it should eject a electron as well as a photon of less energy than incident photon.
In some cases it does eject a photon with a lower wavelength, if it did not do this then the laws of conservation of momentum would not be supported thus disproving many aspects of modern physics. The problem with this is without the experimental evidence or data, it is hard for someone to calculate or predict the new photons wavelength, let alone detect it. The photon would be emitted with such a low energy that the problem would be "How would you detect it?"
You could test the discrepancy of how much energy the electron should have compared to what it does have but even that would be difficult.
Compton scattering occurs on free electrons, i.e. not in a bound state. The equivalent to a Compton scatter would be a scattering of a photon off the field of a solid, momentum and energy balance happening collectively with the total mass of the solid. In the best case it would be a whole atom that the photon would scatter inelastically off, the atom taking the momentum balance and a reduced frequency photon leaving. This would give a continuous spectrum, no cut offs. This could happen only if the Thomson model of the atom were correct , the electrons freely distributed in a continuum . It would not give rise to the photoelectric effect, which gives a discrete electron momentum and implies quantized states for the electron.
In fact the photoelectric effect is one of the lynch pins of proof of the quantized condition of nature in the microcosm. The energy of the photon is constrained by the quantized binding of the electrons, as with a lower energy of the photon no electrons appear.