IRAC cut of $[3.6]-[4.5]>-0.1$ [@Papovich2008] selects sources at $z>1.3$ due to the 1.6peak of stellar emission moving into the IRAC bands at these redshifts. This cut was adjusted to $[3.6]-[4.5]>-0.2$ in order to be sure of selecting as complete a cluster sample as possible, although this also allows more lower-redshift sources to contaminate the sample. Most stars have $[3.6]-[4.5] \sim -0.5$ and so will be removed by this cut [@Galametz2012]. A second cut of $i'-[3.6] > -0.5\times[3.6]+11.4$ [@Cooke2015] was applied to further remove bright low-redshift interlopers and contaminating AGN. To remove faint sources with potentially inaccurate flux measurements, only those with magnitudes brighter than $23.8$mag in $4.5$($5\sigma$ image depth) and $23.6$mag in $J$ ($3\sigma$ image depth) were considered. Any sources referred to hereafter are those that match these criteria. To maximise the overdensity of (proto)cluster sources to field contaminants, we only consider sources within 0.9arcmin of the central RLAGN.

The completeness of our catalogue is a function of F140W magnitude. This image is deeper than the ground-based imaging and is 100% complete to the $J$ band limit of $23.6$mag.

Statistical subtraction
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### Control field

Throughout this study, we use the eighth data release (DR8) of the UKIDSS Ultra Deep 