If you turned base early, cutting off other traffic, what is the safest way to rejoin downwind? Joined the left traffic pattern at a controlled field downwind.  Controller informed me I was number three for landing. Saw traffic on final, turned base, reported to tower "following cessna on final". Controller comes back a minute later and realizes I cut off a plane on final and I was now number two (my mistake here.  I realize now, I think, I should have not maneuvered at all unless I was 100% sure I could see planes 1 and 2 on final). Controller tells me to rejoin the downwind.  At this point, I was still on the base, so I turned right to rejoin the downwind and the plane behind me that was on final passes too close below me while I am executing a turn from base back to the downwind.  Didn't seem safe.  In fact, as soon as the controller told me to rejoin the downwind, that didn't seem safe.  I am not sure what I should have done.  I could have A) had more situation awareness and turned left to get back to the downwind  B) called for a go around (on a base?), moved to the upwind leg (not departure) and rejoined the pattern. C) the controller should have told the plane on final that was behind me to get out of the patter by going around to the upwind leg.  

I realize I caused this issue by maneuvering to base following the wrong plane.  Like most aircraft incidents, it is usually a combination of factors. I caused the first, did I cause the second?  Should I have called for a go around. What should the controller have done?

In the future, I can fix my issue. But what do you do if you are cutting off for whatever reason a plane on final, while you are on base. What is the safe way to get out of the situation.  Ideas?  Thanks
Interesting, but you're not the first to encounter this situation. I understand from what you say that you were going to wedge in between the no 1 and no 2 traffic already established on final. 
Given the circumstances and not time to think about this, the preferred option would be to turn left to rejoin downwind. Assuming no other traffic in the pattern. Then you are turning towards the other traffic. A left turn would have given you a full 270 degree and time to regroup  

Should there have been other traffic on the left base then they would be positioned further downwind from your position. You may become a conflict for them then by turning right.  Equally there may have been traffic joining downwind like you did in which case a left turn could become a conflict to them. 

This is just assumption. I'm just pointing out the need for full on situational awareness particularly in the circuit. Need to know where all traffic is relative to you. 

Finally, I would say it would have been more reassuring for the controller to specify “turn left/right now to rejoin downwind”. If you had made it to final then a missed approach would be the way out and continue rwy heading until advised.