It looks completely outside my experience - I presume this is on a K-jet injection engine? - but all the same I can never resist doing some research on a query, especially if no one else seems to have any ideas.
The nearest picture I can find shows a somewhat similar unit, with a cut-away diagram of the mixture screw. It explains that there is an allan key hole in the plunger, and that the normal allan key spanner allows you to know how far you have adjusted it.
What is meant to happen is that you engage the key in the hexagon hole, then press down the plunger against a spring inside the tube.
You then turn the key to feel the end of the plunger engaging with the adjuster, and then turn it to adjust the mixture.
My guess is that yours is stiff with dirt so the plunger is stuck, or else it is the wrong size allan key and so isn't doing anything. Can you press the spring down?
https://www.landiss.com/mixture.htm