Always-On Backup strategy is it possible to perform differential backup from primary and full and t-log from secondary in Always-On? Is there any data inconsistency issue while restoring these backups file?
Your main problem here would be maintaining what backup was relevant to what, and you would have to continue taking full backups on your primary server in order to reset the differential base and prevent you diff backups from becoming as large as the fulls.

Consider it this way:


Full backup taken on primary (once) 
Differential taken every night   
Full copy_only backup taken on the secondary every Saturday 
Log backups taken on secondary every 30 minutes


In this situation you are never clearing your differential base, this means that the differential backup will get larger and larger over time (you can only run copy_only backups of databases from secondary replicas). Eventually the number of pages changed in the database will reach a sufficiently high number that the differential is as large as the full backup. Not an ideal situation.

I would either go with running full backups nightly, off of your secondary, or take once a week (or more often as needed) full backups off your primary, and use differentials on the other days.