Due to ram-pressure stripping (RPS), jellyfish galaxies are thought to lose large amounts, if not all, of their interstellar medium. Nevertheless, some, but not all, observations suggest that jellyfish galaxies exhibit enhanced star formation compared to control samples, even in their ram pressure-stripped tails. We use the TNG50 cosmological gravity + magnetohydrodynamical simulation, with an average spatial resolution of 50-200 pc in the star-forming regions of galaxies, to quantify the star formation activity and star formation rates (SFRs) of more than 700 jellyfish galaxies at z = 0-1 with stellar masses 10(8.3-10.8) M-circle dot in hosts with mass 10(10.5-14.3) M-circle dot. We extract their global SFRs, the SFRs within their main stellar body versus within the tails, and we follow the evolution of the star formation along their individual evolutionary tracks. We compare the findings for jellyfish galaxies to those of diversely constructed control samples, including against satellite and field galaxies with matched redshift, stellar mass, gas fraction, and host halo mass. According to TNG50, star formation and RPS can indeed occur simultaneously within any given galaxy, and frequently do so. Moreover, star formation can also take place within the ram pressure-stripped tails, even though the latter is typically subdominant. However, TNG50 does not predict elevated population-wide SFRs in jellyfish compared to analogue satellite galaxies with the same stellar mass or gas fraction. Simulated jellyfish galaxies do undergo bursts of elevated star formation along their history but, at least according to TNG50, these do not translate into a population-wide enhancement at any given epoch.
