Will it affect the existing network if another Co-ordinator powers up with same PAN ID?

I have existing network of single Coordinator and 3 Routers of Xbee-S2 with default PAN (here =0)? But, I want to know whether any new Coordinator with default PAN(here =0) powers up within radio range of my network than will if affect my existing network? Do I have to change the PAN-ID to specific number so that my network can be secure?

No, the new coordinator will choose a different 64 bit PAN ID than the existing network all on its own.

Would the new Coordinator choose different 64 bit PAN ID itself? And I am asking would it affect the older network?

Yes, the new Coordinator will select a NEW and Different 64 bit PAN ID all on its own.

But I have connected new coordinator with XCTU. And checked the PAN-ID of new coordinator. But still it shows ID = 0. So how it is gonna change PAN Id?

The PAN ID I am referring to is the 64 bit Operating Pan ID or OP. The ID command is a user settable 64 bit Initial PAN ID.