My son went to Cerdars-Sinai Hospital emergency care when he had a small cut when opening a package with a kitchen knife. The bleeding won't go away, so he went to the Emergency Care; After waiting for about 4 hours, a Phys Assistant sutured the wound, (without completely sealing the wound) and two weeks later, sent a bill for $3000+ as the bill was not covered under the deductible.
Do I have any chance of fighting this with a small court? The hospital refused to reduce the bill.

Your best chance to to go into the office of the hospital or emergency care facility, and ask them for options, give pricing due to low income (perhaps) that would reflect your approved insurance pricing. Your insurance (assume you gave them your card) normally has specific discounts allowed.

But 3000 for a ER room with stitches is really about normal now adays.
My wife had her eye looked at, in a doctors office (about 10 minutes) and the charge was 750 dollars because this was a specialist.

You have no chance of fighting it. Did you have insurance? Why wasn't it covered. Maybe is was simply miscoded by the billing office.

You don’t mention if your son had insurance. A 4 hour wait is pretty short, especially at a hospital of that caliber, but that has nothing to do with billing. Depending on severity, cuts like that aren’t always completely closed to allow for swelling, but that has nothing to do with your bill.

My advice would be to call the billing department and have then walk you through the bill.