We signed a contract and paid in full. The contractor did more work and is demanding more money. Is this legal?

Your son does NOT owe him anything!! The contract states what was to be at what price Both parties agreed and signed. End of story. Tell that contractor that if he continues with the harment you will see him in court. In fact you can tell him that his contract is BS because of the warranty. Who ever heard of a 2 yr. warranty that's only good while the work is being done and when the work is completed it's void. I would also find out if the fact that he owned all 3 companies that gave you estimates is legal. It's almost like he gave no other companies a chance to give an estimate. Tell him The Soprano's is make believe. His actions are giving contractors a bad name. No wonder people think contractors are all mafia related.