Pretty disgusting moment in the stands at the Miami Dolphins game -- when a group of violent thugs began fighting with the family seated in front of them ... even throwing punches over a sleeping child.

Unclear what started the fight ... but at one point a fan in a 49ers shirt stepped in between the child and the attackers and said, "I've got grandkids ... f**king a**hole."

That's when things escalated -- and the Dolphins fans got even more violent -- beating the man down in front of his family.

We're reaching out to police to see if anyone was arrested.