There do exist some spells in Harry Potter that only Voldemort could do such as -
Using the highly advanced art of spell creation, Voldemort was able to create four spells/magical items unique to him alone. These included being able to fly under his own power, creating the infamous drink of despair, the rudimentary body potion, and morsmordre. Theoretically, Voldemort could have done even more which just makes him scarier.
These four spell were known to Voldemort alone and now that he is dead nobody knows how to cast them.There was the spell of Unsupported Flight that Voldemort taught to Snape but he's dead too.
Then there is his rebirth -
Although many have tried, Tom Riddle is the only wizard to achieve complete rebirth. During his lifetime, Tom Riddle split his soul so many times that, when he was finally beaten, there was barely any humanity left. He was just a cursed soul trying to survive, which ultimately led to the scar on Harry's head.
Due to his obsessive fear of passing away, Voldemort was able to put into action a number of contingency plans should he be stripped of his physical self. After interacting with Peter Pettigrew though the ritual, Voldemort was reborn as his physical self, becoming the first and only to do so.
So another ability that is possible but since Voldemort is dead nobody knows how to do it.