The story between the owners of the elder wand goes through a long journey, particularly Albus Dumbledore.
I don't have any idea if the elder wand has a twin at all since it was made by the Death and was bestowed to Antioch Peverell. Based on its details, it was the most powerful wand ever made.
But as we know, in the Harry Potter and the Goblet of Fire, the Priori Incantatem took place. Based on the book, wands are linked if they have the same core.
Harry's wand was 11" long, made of holly, and possessed a phoenix feather core.1 This was described by Garrick Ollivander to be an unusual combination of wand core and wood. The feather was donated by Fawkes, Albus Dumbledore's phoenix. It was revealed by Garrick Ollivander that Tom Riddle's wand core also came from Fawkes, making the two wands "brothers".
I have came across the section of Wikia about the Elder Wand and read this:
It is said to be the most powerful wand that has ever existed, able to perform tremendous feats of magic that would normally be considered impossible even by the most skilled wizards, such as mending another wand damaged beyond normal magical repair. It is known that the Elder Wand's core is the tail hair of a Thestral, a potent yet tricky substance to master that can only be handled by a witch or wizard who is capable of accepting death (many could have handled one), since only by such can it be seen.
It occurred as an unintended consequence of two wands with identical cores having to duel each other
Is there another wand that we know of with a core using Threstral hair from the same Thestral used to make the Elder Wand?