3:45 PM PT -- TMZ obtained the mugshot for suspected killer Loay Abdelfattah Alnaji.

In the booking photo, Alnaji appears to be holding back a smile.

Cops have a man in custody for the death of Paul Kessler ... the Jewish man who was killed at a pro-Palestinian rally in California earlier this month.

50-year-old Loay Abdelfattah Alnaji was arrested Thursday for allegedly killing the 69-year-old man. He's been booked for involuntary manslaughter and is being held at the Ventura County Pre-Trial Detention Facility.

Alnaji's bail is set at $1 million, and officials are still asking citizens to come forward with any information surrounding the fatal incident.

As we reported, Kessler was at a pro-Israel rally on November 5, and a pro-Palestinian rally was going on at the same time nearby -- all stemming from the war between Israel and Hamas.

Law enforcement told us Kessler got into a heated argument with the Palestinian supporters, leading to a physical fight -- and was eventually knocked backward, causing him to fall and hit his head on the ground.