I tried using an external power supply and my arduino serial communication doesn't work, however it does work with the usb. I searched online and found so many related issues but yet not a solved solution. Is there any solution for this problem?
You have not provided enough information.
Post your program and tell us what you are trying to communicate with.
If you are making a serial connection between two Arduinos do you have a GND connection between them?
Serial Input Basics - simple reliable ways to receive data.