help!! how do you raise the door 1/4 inch

The easiest thing to do is to take the door off its hinges and plane it down 1/4 inch. It shouldn't take more than 15 minutes...assuming you have a competent contractor (and I'm not so sure you do based on your post). Good luck.

Agree with looking glass,

Are you talking about the front metal door or just a wood door in the apartment. If it is the metal door they should be able to grind down the door. If the door is from polyform or has a sprayed finish then you do need to remove the door and frame then raise the frame which wil also raise the door

Goodness gracious, what sort of contractor do you have?
Has he done a project before?

I agree. This person seems to be trying to play you to either hire his friend or pay him big for work outside the scope of the job. If he ends up making you an unhappy customer I hope you put in a bad word here.