3:30 PM PT -- The judge has denied Justice's request for a restraining order ... for now. According to the legal docs, there'll be a hearing at the end of the month to determine if Avance will be ordered to stay away.

The docs also shed light on why Justice sought out the protection -- she claims Smith broke into her late father's property last week and took his belongings. She also accuses him of threatening her while John was in the hospital, both by text and in person.

Justice claims Avance is "uncontrollable" and she fears he could be physically violent.

John Singleton's family war is getting serious, and the latest battle is between his daughter and one of his old friends ... TMZ has learned.

According to new legal docs ... John's daughter, Justice, has filed for a restraining order against Avance Smith. Family sources tell us Smith was a very close longtime friend of John's -- so close, John commonly referred to him as his cousin. Smith also worked as a security guard for John from time to time.

It's unclear at this point why Justice wants court-ordered protection from her father's friend.

What's interesting is her request comes one day after Singleton's mom, Shelia Ward, filed an emergency request for control of his assets ... specifically because someone had gone into John's locked office and taken valuables.

We don't know that Avance has anything to do with that allegation.

As we reported, other members of John's extended family have grown suspicious about some of the circumstances surrounding his death -- such as how he initially got to a hospital back in April, and who was with him in the hours before that.

They've hired a private investigator to help them find answers.