Here's how to get rid of mould that grows on the edges of shower screen doors:
Your shower screen's glass panels are probably held in place in their aluminium frames by a clear, elastic epoxy sealant. Many flexible sealants will harden and shrink over time, leaving tiny gaps between the glass and the frames. This "green stuff" is most likely mould growing within or under the sealant, due to the humid conditions in the shower.
It's unhealthy to let bacteria-breeding mould grow freely in places that you and your family use on a daily basis. Scrape out and replace the entire strip of sealant to get rid of the gunk. Before you apply the new sealant, take the opportunity to scrub down the inside corners of the glass and the aluminium frames to get rid of any slimy residue.