The non-diagonal correlators of tensor fermionic current with the vector and axial-vector ones are considered as examples of the two-point one-loop amplitudes modified by a constant homogeneous magnetic field. The tensor current is a fermionic part of the Pauli Lagrangian density relevant for a fermion electromagnetic interaction through its anomalous magnetic moment. Under an assumption that this interaction enters the effective QED Lagrangian, the contribution to the photon polarization operator linear in the magnetic moment is calculated. The other example where a photon interacts with a neutral pseudoscalar particle like an axion is also discussed.