Draconequus are a hybrid species. The only draconequus encountered or at least mentioned in Equestria's long history is Discord. He is most likely a one-of-a-kind creature.
Before Celestia and Luna ruled over Equestria, the land was supposedly held in the grasp of the Draconequus Discord. Discord ruled over Equestria, maintaining a constant state of chaos.
Discord was defeated when Celestia and Luna discovered the Elements of Harmony and used their power against him. He was turned to stone, frozen in an almost jovial pose, suggesting he had not expected the Elements to work.
Before the War
Discord broke free and began to wreak chaos and mischief again. He continued to change the landscape of Ponyville, desiring to make it the chaos capital of the world. Discord toyed with the Mane 6, leading them through a maze where he made them turn their backs on one another. Discord, confident in his victory, seemingly unchallenged, admired the chaos engulfing Ponyville. The Bearers of the Elements used them to once again petrify Discord.
Discord was eventually freed from his stone imprisonment and later showed his true nature, which was a good-hearted draconequus (despite his mischievous nature and his fondness for chaos).
Draconequus are a chimera species like griffins, being a fusion of many more creatures. Discord himself has a lion's paw, a griffin's talon, a lizard tail, a reptile's leg, and a goat's leg. He also has two yellow eyes with red pupils and two mismatched horns on his head. Two mismatched wings, a light blue pegasus wing and a light purple bat wing, adorned Discord's back and his head was roughly pony-esque.
Draconequus have demonstrated their omnipotence, the ability to use powerful, reality altering magic. This magic is exceptionally powerful, with Discord being capable of controlling the sun and moon, altering pony minds, and spawning things from nowhere all with the snap of a finger. The very source of his reality warping abilities is unknown. He is possibly born with it.
In Side Stories
Draconequus have also appeared in Side Stories.
Discord himself appears in Project Horizons, his power diminshed from 200 years of being drained for Flux. He was moved to Hoofington during the war since it was feared the zebra would take him and use him against Equestria. Not wanting to risk his escape, his statue was coated in Star metal making it impossible to escape on his own.
Discord was hooked up to drills and tubes, which drained Flux from his body. He was left alone for 200 years, the machines turned up to full power, draining Discord for Flux. He thanked Blackjack for freeing him and aids in her escape whilst also granting her a perk.
Guise of Chaos
Another Draconequus was captured by the Ministry of Peace in the hopes of using the potential of a Draconequus to heal. The Draconequus was called Pandemonium, his form and power were broken and contained within four Black Cubes, designed to perform specific purposes. Ripple sought out these cubes since Hate wants them and their potential power for his own benefit.