It is now well-established that for the generation of very high brightness beams, required for fourth generation light sources, it is highly advantageous to use injectors based on Radiofrequency photo-guns with very high peak electric fields on the cathode (>120 MV/m). This very high surface electric field leads to the generation of undesirable electrons due to the field emission effect. The emitted electrons can be captured and propagate along the Linac forming a dark current beam, leading to background radiation that can damage the instrumentation and radioactivate components. Consequently, it is important that the emission of these electrons, and their subsequent transportation, is carefully evaluated. Recently, in the framework of the I-FAST project, a high gradient, standing wave, C-band (5712 MHz) RF photogun has been designed and will be realized soon. In this paper, the results of dark current studies and simulations are illustrated. The transport efficiency and the spectrum of the dark current have been evaluated by Particle-In-Cell simulations for different cathode peak field values considering also the effect of the focusing solenoid on the dark current beam.