The Dragon Claw was a weapon Blackjack picked up from the Hoofington Natural History Museum in the area around Chapel. The Claw came from the skeleton of a dragon, found inside the museum. It was still sharp and strong when Blackjack found it.
Blackjack got drunk on Wild Pegasus whiskey and used the claw as a weapon whilst she battled a group of bounty hunters who tried to ambush her at the museum. She levitated the weapon in her telekinetic grip and wielded it on multiple occasions. She once loaned the weapon to Rampage who was a filly at the time, Rampage was too small to wear her armour and couldn't get her other weapons, so Blackjack gave her the Dragon Claw to use.
The Claw stayed with Blackjack until she went to Spike's cave. When she was scaling down the mountain, three Enclave troopers ambushed her. The Claw was disintegrated by their magical beam weapons.