How does electric and magnetic field interchanges in light propagation? We know that magnetism is just a illusion created because of special relativistic effects and there is only electric field which is really there in reality.
so how can we say that this imaginary magnetic field which is just an illusion of relativistic case of charge motion, gets converted into electric field when we talk about light propagation through space?
And why is magnetic field considered as a real field but in reality it's just an illusion??
And how can even this back and forth conversion of magnetic and electric field in light propagation even possible and how can it make sense when talking about light moving in a region of space?
Is it just mathematical or is there something which ties is it reality?
 A: 
We know that magnetism is just a illusion created because of special relativistic effects and there is only electric field...

This is one possible view. Another view is that the magnetic field is as real as the electric field. For an electric field it is necessary to separate charges, and for a magnetic field it is necessary to align charges with their magnetic dipoles. By the way, this is what happened with permanent magnets.
At the level of subatomic particles, the same prioritization works. One can make the circular currents within the (point-like) electron responsible for the magnetic dipole of the electrons. Or one can agree that all subatomic particles have the intrinsic property of a magnetic dipole.

so how can we say that this ... magnetic field ... gets converted into electric field when we talk about light propagation through space?

Electrons both have an electric “aura” and a magnetic dipole and they are responsible for the the emission of photons. It seems to be natural that the photon takes with it energy from both the fields. “Natural” because that is how nature works.

And why is magnetic field considered as a real field but in reality it's just an illusion?

Reasonable question. If you agree with the above explanations, you will not be surprised by the reality of the magnetic field component (besides the electric field component) of photons.

And how can even this back and forth conversion of magnetic and electric field in light propagation even possible ...? How does electric and magnetic field interchanges in light propagation?

This is how electromagnetism works in nature. And now my answer must stop, because the quantization of electric and magnetic fields cannot be discussed here.
