Can one who suffers from obsessive-compulsive disorder (waswasah) and fears swallowing water during ablution while fasting perform tayammum for Dhuhr and Asr prayers?

The cure for obsessive thoughts is to ignore them and not respond to them. If Satan whispers to a person, let him seek refuge in Allah and stop indulging in those thoughts. For ablution (wudu'), rinsing the mouth (madmadah) once is sufficient, and it is not obligatory according to the majority of scholars. If this matter becomes difficult for someone suffering from obsessive thoughts, they can act upon the opinion of those who do not consider rinsing the mouth obligatory. It is advisable for someone suffering from obsessive thoughts to consult a trusted psychiatrist.