What is the ruling on the prayer of one who suffers from the emission of drops of urine after urination, and does not know whether they were emitted during the prayer or after it, which makes him doubt the validity of his prayer?

The basic principle for one who has performed ablution (Wudu') is that their purity remains, and they should not pay attention to doubts and whispers from Satan, unless they are certain that something has exited. What one feels as residual urine during prayer should be ignored, and one should build upon the original state of purity. There is no need to investigate after that, as doing so leads to the continuation of the obsessive whispers (waswasah).