hi,

first of all, it seems you do not read device datasheet carefully. Another thing is that you have not specified the part used. So the next notes are for Atmel`s flash chips. Oh, you said "internal ROM" - do you talk about Mask ROM or Flash memory really?

in the start EA bit is 1 ... if I reset the EA bit to 0. It will automatically start executing the program from external ROM or not.

You should not do this way. If at least one program Lock Bit is programmed then it may cause a malfunction.
See, for protect modes 2 and above, Atmel`s datasheets say:

When Lock Bit 1 is programmed, the logic level at the /EA pin is sampled and latched during reset.
...
The latched value of EA must agree with the current logic level at that pin in order for the device to function properly.

So, it says that you must not change /EA pin level during MCU works.

Now, the second part of your question:

Some part of my program is in internal ROM and remaining is in the external ROM

And so what is the problem?
- put one part of program into internal flash (ROM) memory;
- put extended program code into external flash (ROM) memory;
- tie pin /EA to VCC;
- DO NOT set protect mode 4 otherwise it disables external execution completely;
After reset your program starts to execute code from internal program memory. When it comes out from memory range of internal memory (due jmp, call etc) it continues to execute code from external program memory. Indeed, you need to connect external flash (ROM) memory by correct way with ALE and /PSEN signals (it may/may not require address-decoder as well).

Another note you may pay attention is that in protection mode 2 and above:
- MOVC instructions executed from external program memory are disabled from fetching code bytes from internal memory.

Regards,
Oleg