EXCLUSIVE

If YNW Melly is convicted of murder, he deserves to die ... according to the family of one of his alleged victims -- a stance they're taking despite previously having a close relationship with the rapper.

Melly remains jailed in South Florida as he awaits trial in his double murder case, and prosecutors have already said they will seek the death penalty.

That sits just fine with the family of Anthony Williams. His family tells TMZ, through their attorneys at Steinger, Greene & Feiner ... "If the state of Florida feels the death penalty is warranted in this case then we 100% fully support it."

It's a tragically complicated case for the Williams family. As we first told you, Anthony's family treated Melly like he was one of them, and even opened their home to him. You can see in Melly's mug shot ... the name "Jana" is tattooed on his neck in honor of Anthony's mother.

Still, the Williams family's attorneys add ... "YNW Melly should feel the exact fear and panic he so viciously and consciously brought upon his innocent victims."

TMZ broke the story ... the state of Florida says it has proof beyond a reasonable doubt Melly and Cortlen Henry shot and killed Anthony and another man, Christopher Thomas Jr.

Melly and Henry have both been charged with 2 counts of first-degree murder.