Magnetism is not a relativistic effect. Magnetism is a separate entity although closely related to electricity. In fact in special relativity the electric field and the magnetic field are partially converted into each other when going to a moving frame. You can have a magnetic field without an electric field, and vice versa. These field are not tied to sources. They are entitities in their own right, just as the ripples on the surface of pond may be caused by throwing in a stone, but are not part of the stone-- they exist in their own right.
If you look at Maxwell's equations, the Magnetic field is related to the time derivative of the electric field. Ie, the Magnetic fields acts like the momentum of the electric field ( actually of the electric field potential). In quantum mechanics something and its momentum have an uncertainty relation with each other, and thus the electric and magnetic fields have an uncertainty relation with each other.