  We present a new X-ray spectroscopic study of $22$ luminous
($2\times10^{45}\lesssim L_{\rm bol}\rm /erg\,s^{-1} \lesssim 2\times10^{46}$)
active galactic nuclei (AGNs) at intermediate-redshift ($0.1 \lesssim z
\lesssim 0.4$), as part of the SUpermassive Black hole Winds in the x-rAYS
(SUBWAYS) sample, mostly composed of quasars (QSOs) and type\,1 AGN. Here, 17
targets were observed with \textit{XMM-Newton} between 2019--2020 and the
remaining 5 are from previous observations. The aim of this large campaign
($1.45\,\rm Ms$ duration) is to characterise the various manifestations of
winds in the X-rays driven from supermassive black holes in AGN. In this paper
we focus on the search and characterization of ultra-fast outflows (UFOs),
which are typically detected through blueshifted absorption troughs in the
Fe\,K band ($E>7\,\rm keV$). By following Monte Carlo procedures, we confirm
the detection of absorption lines corresponding to highly ionised iron (e.g.,
Fe\,\textsc{xxv}\,H$\alpha$, Fe\,\textsc{xxvi}\,Ly$\alpha$) in 7/22 sources at
the $\gtrsim95\%$ confidence level (for each individual line). The global
combined probability of such absorption features in the sample is $>99.9\%$.
The SUBWAYS campaign extends at higher luminosity and redshifts than previous
local studies on Seyferts, obtained using \xmm and \suzaku observations. We
find a UFO detection fraction of $\sim30\%$ on the total sample that is in
agreement with the previous findings. This work independently provides further
support for the existence of highly-ionised matter propagating at mildly
relativistic speed ($\gtrsim0.1c$) in a considerable fraction of AGN over a
broad range of luminosities, which is expected to play a key role in the
self-regulated AGN feeding-feedback cycle, as also supported by hydrodynamical
multiphase simulations.
