As we know electrons are charged particles, hence they have a field surrounding them, which has some energy. Now in electron diffraction the electrons have their influence on other electrons and themselves also get affected. So my question is that why this influence of an electromagnetic wave (because of electronic charge) not considered to explain this phenomenon, as that interaction of EM wave may lead to that pattern.
Actually, "this influence of an electromagnetic wave (because of electronic charge)" has been "considered to explain this phenomenon".
Let me note first that in the de Broglie-Bohm interpretation of quantum theory, the trajectory of the electron is defined by the "guiding field", which interacts with (or "feels") the diffraction grating.
On the other hand, I showed how "electromagnetic field, rather than the matter field wave function, can be regarded as the guiding field" and how quantum phenomena can be described in terms of electromagnetic field only (see here (published in Int. J. Quantum Information) and here (published in European Physical Journal C)).
To do this, I showed that the matter field can be eliminated from the equations of the Klein-Gordon-Maxwell electrodynamics and that the resulting equations for the electromagnetic field describe independent evolution of this field. Similar results were obtained for the Dirac-Maxwell electrodynamics. These results remain valid if conserved external currents are added to the right-hand side of the Maxwell equations, which is important for description of diffraction.
Of course, I cannot be sure that the idea described in your question was not considered in some form earlier.
@Sad_lab_rat wrote: "Diffraction occurs due to the wave nature of the electrons and this wave nature is not dependent on the charge of the electron. (To my knowledge)". However, if there is no electromagnetic (or some other) interaction, there is no diffraction.
Let me also add that the Couder's experiments emulating the two-slit experiment using a classical system feature diffraction caused by interaction of a "particle" with the slits via its own surface wave.
An electronic charge doesn't create a wave, it just creates a field. And in electron diffraction the electrons do influence other electrons and themselves. Diffraction occurs due to the wave nature of the electrons and this wave nature is not dependent on the charge of the electron. (To my knowledge)It's just that all particles have this wave nature described by De-Broglie wavelength.
The electronic charge is used to describe how the beam behaves/interacts with the material and some properties of the diffraction pattern do depend on that and they show a different aspect about the material than what light beam would show or neutron beam would show. Hence, you've actually answered your own question in a way I think. :)