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The transitional millisecond pulsar PSR\,J1023+0038 is the first millisecondpulsar discovered to emit UV and optical pulses. Here we present the results ofthe UV and X-ray phase-resolved timing analysis of observations performed withthe Hubble Space Telescope, \textit{XMM-Newton} and NuSTAR satellites between2014 and 2021. Ultraviolet pulsations are detected in the high luminosity modeand disappear during low and flaring modes, similar to what is observed in theX-ray band. In the high mode, we find variability in both the UV and X-raypulse amplitudes. The root mean square pulsed amplitude in the UV band rangesfrom $\sim$2.1\% down to $\sim$0.7\%, while it oscillates in the interval$5.5-12\%$ in the X-ray band. This variability is not correlated with theorbital phase, like what has been observed in the optical band. Notwithstandingthe rather low statistics, we have marginal evidence that variations in thepulse amplitude do not occur simultaneously in the UV and X-ray bands. When theUV pulsed amplitude decreases below the detection threshold, no significantvariation in the X-ray pulsed amplitude is observed. These oscillations in thepulse amplitude could be caused by small random variations in the massaccretion rate leading to a variation in the size of the intra-binary shockregion. Finally, we find that the pulsed flux spectral distribution from theX-ray to the UV band is well fitted using a power-law relation of the form $\nuF_{\nu}^{pulsed} \sim \nu^{0.4}$. This supports the hypothesis of a commonphysical mechanism underlying the X-ray, UV, and optical pulsed emissions inPSR\,J1023+0038.

UV and X-ray pulse amplitude variability in the transitional millisecond pulsar PSR J1023+0038