All the demigods in Percy Jackson and the Olympians: The Lightning Thief have ADHD, with the notable exception of Frank Zhang, who's just lactose intolerant. Grover certainly thinks that Percy has ADHD, as Percy finds it so hard to concentrate in class. He's also irritable, restless, easily distracted; all the symptoms normal associated with the condition. As Grover further points out, ADHD makes you want to get up and go outside and release all that pent-up energy inside you.

In the real world, the world of mere mortals, Percy has been diagnosed with ADHD, but in the world of the demigods it's a different story. Here, the condition is simply an illustration of demigods' heightened awareness and natural aptitude for going out into the world to do battle against fearsome mythical creatures like the Minotaur. What in the mortal world is called ADHD gives demigods quicker reflexes, which comes in pretty handy on the battlefield. Due to the tensing of their muscles, demigods can also sense when their opponents are ready to strike.

Percy actually does not have ADHD.  This is something Annabeth explains to him once he arrives at Camp Half-Blood.  He's always been told that he has dyslexia, but Annabeth explains that he does not; it's just that his brain his hard-wired for ancient Greek writing, and so 21st-century American English simply doesn't compute correctly.  Also, Percy's always been described as impulsive and had a hard time sitting still in the classroom, but Annabeth explains that these are his "battle-field reflexes" and not a lack of impulse control at all.  Finally, Annabeth tells Percy that another reason he seems to have attention problems is that he sees more than the average mortal, not less.  This is another reason he's been told he has ADHD.  She claims that most of the teachers are monsters, and this is one major reason that they'd want Percy on ADHD medicine: they don't want him to be able to see them for what they really are.