There seems to be a short to ground in the wiring somewhere.
why does my turn signal light keep burning out and why is the sockets and plastic lens melted.
Replace turn signal switch. Its grounding when you put turn signals on. I had the same problem and replaced it .Solved issues.
Check or replace the socket
You likely have a frayed wire to the stop light.
Could be there is a short to ground somewhere in the system or the circuit is overloaded with extras. If you have a trailer plug in back take a good look at that area for a short.
Found problem, intermittent short circuit problem in turn signal switch, replaced switch, problem went away.
Try putting in a bigger fuse. Maybe the reason why your blowing is to much going through such a tiny fuse.
Possibly, but it is more likely that one of the bulb sockets is or has been wet, or that one of the wires is shorting to the vehicle chassis.
You probably have a short in one of the light assemblies, turn signal lever, or the wiring.
In the fuse box.
The 2003 Mitsubishi turn signal fuse can be found in the fuse box. The turn signal fuse will be in the second column, fourth from the top.