When electrical fields and magnetic fields couple together, it forms electromagnetic waves. And we can "quantized" it and see each "package" of it as photon. So can electrical fields and magnetic fields be each "quantized" and visualized as a particle (half a photon?)
Short answer, no. Long answer, sort of.
Short answer: No, the E and M fields may be coupled by the Lorentz transformations, but it is only when they work together to make a self-propagating wave that we can call it a particle. To separate them as individual fields is physically meaningless. So giving each field their own particle is equally meaningless.
Long answer: This can be thought of as an "Is the Moon Really There When we aren't Looking at it?" problem. The only way we can observe that an E or M field is present is when it interacts with something via the Lorentz force. So if the field is not interacting with anything, is it really there? In advanced physics, that answer turns out to be a resounding "no". What we can say is that the E or M field interacts with objects via a photon. That is, the magnetic or electric field can be said to exists, but we can also say that the source of this field is interacting with our sensors or other particles by exchanging photons to produce a force. Thus, to answer your question, we can in a way "quantize" the separate fields and visualize them as a particle, but only if we visualize them not as fields but the exchange of photons between the sources of the field and the objects influenced by it. But full photons, not half a photon.