If the backup can be cleared with a plunger every time this happens, and the toilet is several years old, chances are the trap has become calcified. This makes the lining of the trap rough and it snags paper as it tries to travel through the trap.
There are two things you can do here, one, replace the toilet, or try some CLR (calcium and lime remover) available a your local DIY warehouse. Remove the water from the trap and pour the CLR into the bowl until it reaches it's normal level. I make a little mark with a sharpie before removing the clear water, so when I pour in the CLR, the level is the same. Leave the CLR for about 18 to 24 hours, then flush as you normally would. Test the effectiveness of the treatment by flushing 30 sheets of paper down the toilet two times in a row. If the paper goes down without backing up. you're good to go. If it backs up again, you will need a new toilet. There is still a chance the problems you describe could possibly be an issue with your sewer line below the floor, or some object has fallen into the trap causing the paper & waste to get caught on it's way through. I once remove a no2 pencil that was too long to pass through the toilet but was floating inside the trap because it was wood! lol
I made three trips to the customers home before taking the toilet out to the lawn and turning it upside down to discover that %^&*$ pencil.