There are two types of current between parallel plate capacitors.
One type of current is conduction current due to conductivity of the medium between plates.
Other type of current is displacement current due to change in electric field .
Conduction current and displacement current will be equal in magnitude.
Since displacement current ε(∂E/∂t) is in opposite direction of conduction current
because (∂E/∂t) is proportional to (∂Q/∂t) but (∂Q/∂t) is negative.
Hence magnetic field due to conduction current and magnetic field due to displacement current
cancel each other.
Net magnetic field is zero