I'm planning to use the AVR/Interrupt to give priority for received serial data through UART RX1 pin at Arduino DUE. At the same time will be another data coming in from other serial too. My question is, if i use the the ISR macro, is there any possibilities that the hardwareSerial library will overwrite the ISR micro when i use the Serial1.begin? does the ISR Macro will be affected if initiating other serial port like Serial2.begin?
You'd get a compile error if you try to define the same ISR in two places. You'd have to modify the hardware serial class itself, or create a library with your implementation.
You also don't need to. Your whole proposal is unnecessary - the time it takes for the ISR to run is very small relative to the time between characters. It is not realistic for there to be a case where one serial port being busy prevents servicing of another.
The rest of your code could drop the ball by letting data pile up until it filled one of the ring buffers, at which point characters would be lost... but that's a bug happening outside the ISR...