Head Summoner Galatea:
If you are serious about challenging a more advanced summoner, here are some likely candidates here in Aden.
Summoner Almorsis recuperating on Talking Island at the moment. Summoner Basillia, rumor has it, is preoccupied with studying new summoning magic at his seaside home in southern Gludio.
The Elf, Summoner Camoniell, lives in retirement in his villa in southern Dion; I have heard that he has had some sort of bad experience lately. Summoner Celestiel once lived in the Ivory Tower, but apparently something happened in his hometown and he hastily returned to the Elven Forest.
The Dark Elves, Summoner Brynthea and Summoner Belthus, seem likely adversaries for you, but you may have trouble actually finding them. The last I heard, Brynthea is in the eastern part of Giran and Belthus is somewhere in the Cruma Marshlands.
All of these summoners are very proud, so when an apprentice summoner such as yourself challenges them to a duel, they may simply scoff at you. Eventually, however, their vanity may win out and they will accept your challenge to demonstrate their own superiority.
Here, take this Dimension Diamond. You can trade it to the village gatekeeper for something special that may help you on your journey.