In the original story of Aladdin, his nationality is often not explicitly defined. It's more focused on the magical and adventurous aspects of the tale.
The nationality of Aladdin in the original story is Chinese. The story is filled with details that suggest a Chinese origin. For instance, the descriptions of the settings, the architecture, and some of the cultural practices mentioned in the original tale are very much in line with what was known about China during the time the story was created. This gives a strong indication that Aladdin was meant to be Chinese in the original narrative.
In some Western versions, Aladdin's nationality is not as clearly Chinese as in the original. They sometimes make it more generic Middle - Eastern. This is because Western adaptations often try to fit it into a more general 'exotic' Middle - Eastern - like setting for marketing purposes.
In the original story, Aladdin's first wish is to be saved from the cave where he finds the lamp. His second wish is often to become a prince so that he can marry the princess. And his third wish is usually to free the Genie from the lamp.