5:32 PM PT -- TMZ obtained the mug shot for Richard Roberts, who we're told is currently in jail.

11:23 AM PT -- Montgomery PD says the riverfront brawl has resulted in criminal charges -- with three white males getting rung up. However, there's still more potential charges to come ... and cops consulted with the FBI to determine if the incident was a hate crime.

Chief of Police Darryl Albert says 13 people were detained Saturday, and brought in for questioning after the fight but they were all released. After further investigation, warrants were issued for three men -- 48-year-old Richard Roberts (2 warrants for 3rd-degree assault); one warrant for 23--year-old Allen Todd (charged with 3rd-degree assault); and one warrant for 25-year-old Zachary Shipman (charged with 3rd-degree assault).

Albert says one of them is already in custody, and two are set to turn themselves in later today for booking and processing.

Now, as far as the Black man who was hitting people with a chair -- Chief Albert ID'd him as Reggie Gray, but notes he has not been charged yet ... although, MPD wants him to come in for further questioning.

One last thing ... Albert says Montgomery PD was consulting with the FBI to determine if hate crime charges are applicable or not. The investigation is ongoing -- and it sounds like this is far from over.

The Alabama riverfront brawl landed people in handcuffs, but not necessarily in jail -- which may all change starting Tuesday ... 'cause cops are about to provide a big update.

Montgomery PD is holding a press conference, where they're expected to discuss 4 arrest warrants that were issued Monday in relation to the melee that went down over the weekend. The names of the individuals who are now wanted and the exact charges they're facing have yet to be released ... that's presumably what the police are going to address.

Many assumed the fight participants were arrested on the spot Saturday at Riverfront Park -- where there's tons of video showing folks in police custody. However, authorities have since clarified that all those people were simply detained that day ... and none were arrested.

Montgomery's mayor signaled in his statement from this weekend that more consequences were coming -- and he seemed to point the finger at the group that originally started beating up the security guard/dock worker, who was trying to get them to move their boat.

Of course, all hell broke loose after that ... several others came running to this guy's defense, and a lot of 'em started whooping on the pontoon crew, pretty brutally as it turned out.

The whole thing ended up playing out along racial lines -- Black versus white, it seemed -- and there was a lot of commentary about it in the aftermath, with many championing what they perceived as an act of solidarity among the Black folks.

Time will tell who gets dragged into court over this, and how much trouble they're in.