Does the magnetic field lie in the Wave-Particle duality? There is Wave–particle duality. According to this theory, light is a wave and a particle at once.
What about magnetic field? Can it be so, that it is also a wave and particle, but this particle has not yet been discovered?
Is magnetic field discrete?

 A: Current physics formulation has two frameworks. One is the macroscopic one, in dimensions comensurate with our physical faculties of observation, larger than micrometer sizes. This is the classical framework which was studied and formulated mathematically until the beginning of the twentieth century. Since then we have found out that the classical framework emerges from a more fundamental one,  the quantum mechanical framework that describes the microscopic world, molecules, atoms, nuclei etc.

There is Wave–particle duality. According to this theory, light is a wave and a particle at once.

The statement on wave particle duality is a statement on the quantum mechanical framework. In that framework yes light can behave like a billiard ball ( particle) or like a wave ( with a sine/cosine wave like behavior in the possibility of detecting it).

What about magnetic field? Can it be so,

The magnetic field is a macroscopic concept described by the classical electromagnetic theory.

that it is also a wave and particle, but this particle has not yet been discovered? 

so no, it is not a wave and a particle in the quantum mechanical sense. The magnetic field emerges from the underlying quantum mechanical framework in a strict mathematical way, that you might learn if you continue your physics studies, but has no description as a quantum mechanical/wave-particle. 
As a handwaving explanation, the magnetic field emerges from the virtual coherent overlapping  of innumerable photons, which photons are the particle/wave form  of the electromagnetic force in the quantum mechanical framework. Virtual because of the mathematics involved which do not allow them to light up as a light source :) but remain tied up to the atoms and molecules creating the classical field. Non virtual photons do obey the wave particle duality, depending on the way they are  detected.

Is magnetic field discrete?

It is discrete only in the sense that it is generated by individual atoms that carry a magnetic field, not in the sense of the particle/wave duality.
A: The electric and magnetic field are the manifestation of electro-magnetic field. If you change your reference frame (Lorentz transformation) magnetic field may vanish and electric field appears. Hence more fundamental thing is the electro-magnetism. On that perspective the particle of this field exist, they are called Photons (Light) !  
