Is there any way...
 

that I can play a copied game with the use of any mod chips or accesories?

Do you mean without if you mean with yes surely you can cos thats what its for to play you backups :)

i mean without...

hmm well the older way was to boot the psx with an original game then during the boot sequence you rip out the disk and slam in your copy to continue the boot sequence. It is a little bit harder to do now-a-days with the new games and recent psx's. better to modchip your psx - less damage in the long run