man. ur system partition may be broken. I suggest u to download newest stockrom galaxy core single sim i8260 or dual sim i8262 depend on ur device variant on google and find tutorial to flash it with correct step by step via odin.
Then after all complete, u can install twrp again and make backup and install new custom rom galaxy core. Just remember type of the custom rom is same variant with ur type single sim i8260 or dual sim i8262
If problem persist, i have no idea. Just go to samsung service center.
Sent from my GT-I8262