After misidentifying traffic pointed out by the tower; a PA28 Instructor and Student Pilot suffered an NMAC with a C172 while entering the pattern.

Narrative

With Runway 27L in use; we entered the pattern [and] we were instructed to fly westbound. While westbound outside the pattern ATC instructed us to follow the Skyhawk ahead and to our right on downwind. There was a Skyhawk nearly abeam us and to the right; so I assumed that was the traffic we were to follow. However; there was an additional Skyhawk which ATC was referencing. After we began turning toward the downwind; ATC told us to turn left immediately. I took control of the airplane and maneuvered back to downwind. I couldn't accurately state how close we were to the other traffic but it was certainly what I would consider a near miss.One contributing factor was instructor fatigue. This flight was the last of four activities of the day and my level of alertness and judgment was lower than if it were the first flight of the day. Additionally; after the ATC instruction; I found what I thought was my traffic but did not double check as I normally would. Another contributing factor is a limitation of the airplane we were flying. As we began the turn into the pattern; the conflicting traffic was obstructed by the wing; limiting our ability to see and avoid.