We know that a moving charge produces a magnetic field. But which frame of reference it must move to produce magnetic field? And also if a charged particle moves in a magnetic field, magnetic force acts on it. In which frame of reference it must move to feel a force?
We know that a field that is purely electric in one frame of reference will, in general, be a mix of electric and magnetic fields in relatively moving reference frames.
In a frame of reference in which an isolated point charge is not moving, the field of the point charge is purely electric.
But, as observed from a relatively moving reference frame, the field will in general, have a magnetic component.
Honestly, I don't quite understand the motivation for your question. A charged particle that "feels" a force in one frame must according to any frame.
Now, in the particle's frame of reference, the particle is by definition at rest and thus the force is purely electric in nature. From a relatively moving frame, the force has a magnetic component. Recall from above that the electric and magnetic fields "mix" as we transform from a reference frame to a relatively moving reference frame.
Based on a comment below from the OP, I think I now see what the question actually is so the following is an attempt to answer that.
If a charged particle is at rest in a purely magnetic field, there is no electric or magnetic force on the particle. The particle is not accelerated; there is no net force on the particle.
But, from some relatively moving frame of reference, the charged particle is moving in a magnetic field so there must be a magnetic force acting on the particle.
However, in this moving frame, what was a purely magnetic field is now some mix of electric and magnetic fields.
And, since there is no net force on the particle, it must be the case that the electric force acting on the particle is equal and opposite to the magnetic force.