A cold-hearted crook shoved a gun into the face of a cute 3-month-old baby in sun-soaked Central Park yesterday as he ambushed the child's mother and mugged her, cops said.

"Give me your rings!" the **** demanded before swiping Catherine Collins' two engagement rings, one a $6,000 Tiffany platinum band with several sparkling diamonds.

"The sucker actually points the gun at my baby," said Collins, 34, a Manhattan film producer.

Her blue-eyed boy, Jackson, seemed unfazed during the nightmare mugging, keeping silent the entire time inside his stroller.

"He's a real New Yorker - now that he's been mugged finally and he's not even 4 months old," his relieved mom quipped.