We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily parallelizable and thus save run time. The presented solver is then verified using two different approaches of manufactured solutions. The test setup used for this effort is a pinch geometry with ITG-like electric potential, containing one non -periodic and two periodic directions, one of which will be discrete Fourier transformed. The results of these tests show that in all three dimensions the L2 -error decreases with a constant rate close to the ideal prediction, depending on the degree of the chosen basis functions.