I would like to know how many weeks my article, Review of School Climate Research, has been the most read in my department , Psychology, Fordham University,
Ann - as far as I am aware this information is not available on Research Gate. I am always the most read in my department - so that is easy for me to work out. However, I'm not always the most read in my institution. I wanted to know the same thing for how often I was top in my institution - but could not find a way of accessing previous history. RG seems to have a heavy focus just on the current week.
The statistics of the Department of Psychology at Fordham University are at https://www.researchgate.net/institution/Fordham_University/department/Department_of_Psychology/stats. The statistics for the week of 8–15 September show 86 reads for A Review of School Climate Research. (ResearchGate does not provide the statistics of Top Read Publications for a longer period.)
I would say to contact Research Gate directly rather than asking other users. They do respond to inquiries, in my experience. Maybe you should ask about 2-3 related metrics so as to get the most out of the contact. For example, the number of reads and the number of full-text reads you've had per week. The profile page only gives this information for the past couple of months, but presumably older data are available somewhere.