D01 TRACON Controller reported the new RNAV Y approach for Runway 16R at DEN is causing considerable confusion for flight crews and recommended the procedure be modified.

Narrative

I was working Front Range 1 with Aircraft X that was assigned the RNAV Y 16R about 4 miles ahead of Aircraft Y that was assigned the RNAV Z 16R. The plan was to let Aircraft Y take the RNAV Z (short curved approach) and take Aircraft X on the downwind so they could join 1;000 feet below the 16L final on a visual. This is a common best equipped; best served situation we do all the time.After Aircraft X entered my airspace I gave them a descent and then cleared Aircraft Y behind for the RNAV Z. Aircraft X read back descend 8;000 but then I noticed they were flying the RNAV Y track to fix (TF)/curved leg instead of staying northbound on the STAR. They had also slowed down (basically self-cleared themselves to slow) which made them a conflict with Aircraft Y behind. I had to turn Aircraft X left heading 330 and maintain 8;000 to keep them clear of the parallel traffic.When I asked what they were doing; it was clear they didn't load the approach correctly and were self-cleared for the RNAV Y and had put in the TF leg off the STAR. This was the 3rd airplane that same day I saw make that same turn in error. This new RNAV Y (changed about a month ago) continues to be confusing and creates a dangerous setup when traffic is busy. The current fix of NOTAM the TF portion out solution isn't working. We need some help from outside our building to address and fix the issue.Split the RNAV Y into two approaches. Keep the current RNAV Y with transitions; and publish a new straight-in RNAV X (like the old one from over a year ago). That would prevent crews from flying the wrong TF leg and cut down the confusion. The straight-in and curved portion was already flight checked so implementation should be doable pretty quick. I think we just need some higher level help.