Exploiting broad- and narrowband images of the Hubble Space Telescope from the near-UV to I-band rest frame, we study the star-forming clumps of six galaxies of the GASP sample undergoing strong ram pressure stripping. Clumps are detected in H{alpha} and near-UV, tracing star formation on different timescales. We consider clumps located in galaxy disks and stripped tails and formed in stripped gas but still close to the disk, called extraplanar. We detect 2406 H{alpha}-selected clumps (1708 in disks, 375 in extraplanar regions, and 323 in tails) and 3745 UV-selected clumps (2021 disk, 825 extraplanar, and 899 tail clumps). Only ~15% of star-forming clumps are spatially resolved, meaning that most are smaller than ~140pc. We study the luminosity and size distribution functions (LDFs and SDFs, respectively) and the luminosity-size relation. The average LDF slope is 1.79+/-0.09, while the average SDF slope is 3.1+/-0.5. The results suggest that the star formation is turbulence-driven and scale-free, as in main-sequence galaxies. All of the clumps, whether they are in the disks or tails, have an enhanced H{alpha} luminosity at a given size, compared to the clumps in main-sequence galaxies. Indeed, their H{alpha} luminosity is closer to that of clumps in starburst galaxies, indicating that ram pressure is able to enhance the luminosity. No striking differences are found among disk and tail clumps, suggesting that the different environments in which they are embedded play a minor role in influencing the star formation.