[jtruong]

I know that in a uniform magnetic field, a charged particle moves in a circular path.

Whenever something is moving in uniform circular motion

F= mv^2/r

In other words, centripetal force is proportional to v^2.

However, it is magnetic force that supplies centripetal force which is given by the formula

F=qvB

In other words, magnetic force that supplies centripetal force is proportional to v.

Is force in this case proportional to v^2 or v ?

[Schrödinger]

It is the magnetic force that provides the centripetal force
mv^2/r = qvB
Given certain values of q and B, magnetic force is proportional to v.

When the particle is moving in a circle of a given radius, then the centripetal force is proportional to v^2.