I restricted the background data on my phone during last bill cycle for most of the apps. However i have unchecked them now but it still doesn't seem to be working. I have checked and then unchecked the"restrict background data" multiple times. As a result am unable to receive mails or notifications on apps unless i open them. I have also rebooted my phone but with no result. Can you please suggest something.
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Hi ultron, and welcome to Android Forums 
In addition to the setting suggested by ooberandy, you could also try Settings > Apps > (menu) > Reset app preferences. This will reset any settings related to disabled apps, disabled notifications, default applications, and (most importantly) background data restrictions without erasing any data. It could be that the apps have the "restrict background data" still enforced somehow, and resetting it here should clear that up. :thumbup:
Good luck!
In addition to the setting suggested by ooberandy, you could also try Settings > Apps > (menu) > Reset app preferences. This will reset any settings related to disabled apps, disabled notifications, default applications, and (most importantly) background data restrictions without erasing any data. It could be that the apps have the "restrict background data" still enforced somehow, and resetting it here should clear that up. :thumbup:
Good luck!