Context. The pressure exerted by the ambient hot X-ray gas on cluster galaxies can lead to the presence of ram pressure stripped (RPS) galaxies, characterized by asymmetric shapes, and, in some cases, tails of blue stars and/or X-ray gas, with increased star formation. Aims. With the aim of increasing the known sample of RPS galaxies at redshift z ∼ 0.5, notably higher than most RPS samples presently known, we extended our searches for such galaxies to the cluster MS 0451.6-0305. Methods. Our study is based on Hubble Space Telescope (HST) imaging in the F814W band (corresponding to a restframe wavelength of 529 nm), covering a region of about 6 × 6 Mpc², an eight magnitude ground-based catalogue with photometric redshifts, and a spectroscopic redshift catalogue. We defined as cluster members a spectroscopic redshift sample of 359 galaxies within ±4σ_v of the mean cluster velocity, and a photometric redshift sample covering the [0.48, 0.61] range. We searched for RPS galaxies in the HST images and tested the error on their classification with a Zooniverse collaboration. We also computed the phase space diagram of RPS candidates in the spectroscopic sample. Finally, we ran the LePhare stellar population synthesis code through the GAZPAR interface to analyze and compare the properties of RPS and non-RPS galaxies. Results. We find 56 and 273 RPS candidates in the spectroscopic and photometric redshift samples, respectively. They are distributed throughout the cluster and tend to avoid high density regions. The phase space diagram gives the percentages of virialized, backsplash, and infall galaxies. RPS galaxy candidates typically show rather high star formation rates, young ages, and relatively low masses. We compare all our results to those previously obtained for the massive merging cluster MACS J0717+3745, at a similar redshift. Conclusions. This study increases by at least 56 objects if we only consider galaxies with spectroscopic redshifts, and probably much more if galaxies with photometric redshifts are taken into account. This study increases the number of RPS candidates at redshift z > 0.5, and confirms that they host, on average, younger stellar populations and strongly form stars when compared with non-RPS counterparts. The fact that RPS candidates with spectroscopic and with photometric redshifts have comparable properties shows that large samples of such objects could be gathered based on multi-band photometry only, a promising result in view of the very large imaging surveys planned in the coming years (DES, Euclid, LSST, etc.).