The magnetic force does no work [*], so the work it does is clearly independent of path.

But the magnetic force can't be written as the gradient of a scalar potential (because it depends on the charged body's velocity).

For this reason, some consider the magnetic force to be conservative, whereas others do not.

Please note that there is a case where the magnetic force does work: when it acts on a point dipole such as an electron. Here the potential is − m ⋅ B where m is dipole moment. If the orientation of the dipole is held fixed, the magnetic force is unambiguously conservative in this case.