I would like to know how do I apply for a nose job done by resident?

In an academic training facility, residents operate with the supervision of attending physicians. If you are interested in having a resident involved with your care, I suggest you seek a physician at an academic center.
I would also suggest that you seek a consultation with a surgeon who is experienced in rhinoplasty. It can be a challenging surgery even in the most experienced hands.  If cost is an issue, you may seek a consultation with multiple physicians, even those in private practice, to find the right surgeon to help you obtain the functional and cosmetic results you desire as well as at a price point that is comfortable for you.

You could contact a medical school near you and find out if they have a residency cosmetic clinic that offers reduced fees to patients who are willing to have their surgery done in a training problem.  Be sure to discuss your goals and concerns with the supervising board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search.