ABSTRACT We present the X-ray analysis of the largest flux-limited complete sample of blazar candidates at z > 4 selected from the Cosmic Lens All Sky Survey (CLASS). After obtaining a nearly complete (24/25) X-ray coverage of the sample (from Swift-XRT, XMM–Newton, and Chandra), we analysed the spectra in order to identify the bona fide blazars. We classified the sources based on the shape of their Spectral Energy Distributions and, in particular, on the flatness of the X-ray emission and its intensity compared to the optical one. We then compared these high-z blazars with a blazar sample selected at lower redshifts ($\bar{z}∼ 1$). We found a significant difference in the X-ray-to-radio luminosity ratios, with the CLASS blazars having a mean ratio 2.4 ± 0.5 times larger than low-z blazars. We tentatively interpret this evolution as due to the interaction of the electrons of the jet with the Cosmic Microwave Background photons, which is expected to boost the observed X-ray emission at high redshifts. Such a dependence has been already observed in highly radio loud AGNs in the recent literature. This is the first time it is observed using a statistically complete radio flux limited sample of blazars. We have then evaluated whether this effect could explain the differences in the cosmological evolution recently found between radio and X-ray selected samples of blazars. We found that the simple version of this model is not able to solve the tension between the two evolutionary results.