That’s an interesting request, anon, because I don’t see Royalty and Powerful as being synonymous. I’ve read plenty of BAMF!Merlin fics where he’s just a servant (and others where he’s a prince). But I’ll give you a bit of both:
Royalty!Merlin who is also Powerful!Merlin
An Bruane by sassafrasx
Word Count: 13,998
Summary: Camelot has been at war with the Druids for decades, ever since Arthur’s birth, and neither Merlin nor Arthur have ever known anything else. But destiny is a many twisted thing and when their paths are thrown on a collision course, there will be a reckoning.
Comment: Merlin isn’t a Prince, but he’s definitely the leader of the Druids, plus he’s powerful.
Forlæte - The Surrender by Gbean
Word Count: 26,587
Summary: Arthur and Merlin are princes of two opposing races due to a conflict that started with their parents and plunged the planet into a brutal civil war. Arthur belongs to an ancient race of dragon shapeshifters. Merlin is the most powerful sorcerer to ever live. Arthur and Merlin are placed into an arranged bonding with hopes that it will bring peace to their nations. The bond between a shapeshifter and a sorcerer is an ancient ceremony to keep the sorcerer’s magic from flaring out of control. Is Arthur strong enough to keep Merlin’s magic from consuming him? Will the two men give into their feelings for one another?
This is part 1 of 2 from the Draka Series by Gbean
Comment: Prince!Merlin and Prince!Arthur. Plus it’s a Space AU (yesssss)
The Beltane Cycle by astolat
Word Count: 27,725
Summary: There is a story that is not told in Ealdor anymore, not for many years now, a story about Beltane Eve.
Comment: Merlin isn’t exactly a Prince, but he is the son of a God-like creature, and I think that’s close enough, plus the usual Powerful!Merlin
The Crown of the Summer Court by asolat
Word Count: 24,339
Summary: “The king sent me to get you,” Merlin said, with a tone that implied strongly that he wasn’t rolling his eyes where Arthur could see, but just wait until his back was turned. “He said you’re to get changed into formal clothes and meet him in the Great Hall, there’s a delegation coming from the Summer Court.”
Comment: Elven Prince!Merlin; Canon AU. This is also a kind of Merlin Classic (also by asolat) and its one of the best Canon AUs I’ve read.