Light aircraft student pilot reported an NMAC with another light aircraft in the pattern at SYR due to misidentifying the aircraft cleared to follow.

Narrative

On right downwind for Runway 10 in Aircraft X; Tower cleared me to land number 3; following Aircraft Z on short final and a Aircraft Y on base leg. I acknowledged; confirmed traffic in sight; and began my pre-landing checklist. At this point; I misidentified an object off my right side as the Aircraft Y on final. Believing I was properly sequenced; I began my base turn. Tower then advised that I had cut off Aircraft Y. I observed Aircraft Y slightly to my left and approximately 200 feet above. I descended to maintain separation and advised Tower that I had the traffic in sight. Tower instructed me to re-enter a left downwind for Runway 10; then cleared me to land.Assessment: I failed to maintain continuous visual contact with the traffic I was instructed to follow and did not adequately verify its position before initiating my base turn. This was an unacceptable lapse in traffic awareness and sequencing compliance.Corrective Action: I accept full responsibility for this error. I will undergo remedial training with my instructor focusing on traffic sequencing; scanning techniques; and positive identification of aircraft before maneuvering. I will not be authorized for solo flight until this training is complete.