Is what the questioner suffers from—the emission of drops of urine after urinating—a form of waswas (obsessive whispering), and how can he rid himself of it? Should he disregard these drops that are emitted and are they excused? Is his prayer valid?

The cure for obsessive whispers (waswas) is to ignore them and not pay them any attention. So, if you doubt that drops have come out, do not pay attention to the doubt; rather, build upon the original state, which is purity. If you are absolutely certain that some urine has exited, then you must perform istinja (washing the private parts) and then wudu (ablution). The Malikis hold that it is not obligatory to purify these drops if they come out every day, even once, and prayer is valid with their exit, provided one performs ablution after they exit, as long as the person is not afflicted with سلس (urinary incontinence). For someone suffering from waswas, it is permissible to adopt the easiest and lightest opinions to remove hardship.