Dear Student,
Current is the rate of flow of charge. So, flow of electrons in a conductor results in current. But the direction of current is opposite to the direction of electron.
While neutrons are chargeless. So, flow of neutrons don’t constitute any current. Even though it is not possible to make neutron flow in any situation.
Thus, current carrying conductor producing a magnetic field around it is similar to magnetic field produced by a moving electron.
Regards