Luigi Mangione Returns to Court for Extradition Hearing, Denied Bail

1:50 PM PT -- Luigi Mangione has obtained legal counsel and is fighting the extradition to New York ... but has 14 days to apply for the challenge, known as a writ of habeas corpus.

According to court documents obtained by TMZ ... Judge David Consiglio will schedule a hearing ... if and when the application is filed.

Mangione will be held without bail at SCI Huntingdon until then.

Luigi Mangione, the suspected killer in the fatal shooting of UnitedHealthcare CEO Brian Thompson, has returned to court ... with the government's goal to have him extradited to New York City.

Mangione has been denied bail Tuesday -- and he's fighting the extradition to New York. As he arrived at the Blair County Courthouse in Hollidaysburg, Pennsylvania, he began shouting toward reporters before officers rushed him into the building.

The murder suspect -- who has sparked both ire and admiration for his alleged involvement in the slaying of an insurance executive in midtown Manhattan last week -- returned to the courthouse Tuesday ... where a judge kicked off the extradition process to send LM to the Big Apple to face charges there.

Mangione previously appeared at the courthouse Monday evening, where he was charged with forgery, carrying a firearm without a license, tampering with records or identification, and providing false identification to law enforcement ... after being arrested in a McDonald's in Altoona earlier in the day.

New York prosecutors later hit Mangione with a second-degree murder charge for the shooting of Thompson.

Mangione also faces a number of other charges in New York ... including possession of a loaded firearm, possession of a forged instrument, and criminal possession of a weapon.

We're sure more developments are to come ... so, stay tuned.