What is the ruling on a substance resembling semen being discharged from time to time, and drops of urine being discharged intermittently from time to time after urination?

The preponderant view is that this discharge is "wadi," and it is impure, necessitating istinja (definition) (washing the private parts), purifying anything it contaminates, and performing wudu (ablution). If it is semen discharged without lust, it does not necessitate ghusl (definition) (ritual bath) but only wudu. As for urine drops, they are impure and necessitate istinja and wudu. It is recommended to relieve oneself a sufficient time before prayer to allow the drops to stop, then purify oneself. If they do not stop until after the congregational prayer has passed, then pray individually after they stop. If the discharge of urine or wadi continues throughout the entire prayer time, then you are afflicted with incontinence ( سلس), and you must perform wudu after the time for prayer begins, and protect yourself by tying a cloth over the area. There is no harm in going to the mosque if you are confident you will not contaminate it. Treatment is recommended.