Lil Tjay allegedly started a fight that led to his associate shooting Offset ... this according to police.

According to the probable cause affidavit ... cops claim at around 7:22 PM ET Monday, Lil Tjay "directed members of his party to start a fight with another group of males" at the Seminole Hard Rock Hotel and Casino in Hollywood, Florida.

Police say during the altercation one of Lil Tjay's associates pulled a gun and fired ... injuring Offset.

The docs say cops have reviewed security footage of Lil Tjay hopping out of his vehicle, pointing out Offset, and leading his group over to the rapper, where the fight broke out. They also claim Lil Tjay filmed the incident on his phone.

The fight between Lil Tjay and Offset's friends went on until police arrived, cops add.

As you know ... Lil Tjay was arrested and booked into the Broward County Jail on a charge of misdemeanor disorderly conduct-affray. He was released Tuesday -- at which time he called Offset a "rat" ... watch the video above.

Offset's still recovering in a local hospital ... though he was well enough to be wheeled outside for a cigarette this morning.