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Data from the SPectroscopic IDentification of ERosita Sources (SPIDERS) aresearched for a detection of the gravitational redshifting of light from$\sim\!20\,000$ galaxies in $\sim\!2500$ galaxy clusters using threedefinitions of the cluster centre: its Brightest Cluster Galaxy (BCG), theredMaPPer identified Central Galaxy (CG), or the peak of X-ray emission.Distributions of velocity offsets between galaxies and their host cluster'scentre, found using observed redshifts, are created. The quantity$\hat{\Delta}$, the average of the radial velocity difference between thecluster members and the cluster systemic velocity, reveals information on thesize of a combination of effects on the observed redshift, dominated bygravitational redshifting. The change of $\hat{\Delta}$ with radial distance ispredicted for SPIDERS galaxies in General Relativity (GR), and $f(R)$ gravity,and compared to the observations. The values of $\hat{\Delta}=-13.5\pm4.7$ kms$^{-1}$, $\hat{\Delta}=-12.5\pm5.1$ km s$^{-1}$, and$\hat{\Delta}=-18.6\pm4.8$ km s$^{-1}$ for the BCG, X-ray and CG casesrespectively broadly agree with the literature. There is no significantpreference of one gravity theory over another, but all cases give a cleardetection ($>2.5\sigma$) of $\hat{\Delta}$. The BCG centroid is deemed to bethe most robust method in this analysis, due to no well defined centralredshift when using an X-ray centroid, and CGs identified by redMaPPer with noassociated spectroscopic redshift. For future gravitational redshift studies,an order of magnitude more galaxies, $\sim\!500\,000$, will be required-apossible feat with the forthcoming Vera C. Rubin Observatory, Euclid andeROSITA.

Gravitational redshifting of galaxies in the SPIDERS cluster catalogue