What is the ruling of Islamic law regarding how to deal with the frequent discharge of prostatic fluid (madhy), which leads to physical and psychological exhaustion? Are there any medical or jurisprudential solutions for this problem, which causes physical pain and affects the soundness of prayer and self-confidence?

You may be afflicted with waswasah (whispers from Satan), so you must ignore them. The thick liquid that comes out after or without urination is Wadi, which is impure and necessitates Istinja (washing the private parts) and Wudu (ablution). As for Madhi (pre-seminal fluid), it is discharged during thought or foreplay. If what you mentioned is correct, then consult doctors. If you find enough time for purification and prayer within the prayer time, then you are not afflicted with سلس (urinary incontinence), and you must perform Wudu and pray within this time. The Maliki jurists offer leniency regarding fluid that is discharged involuntarily, as they do not necessitate purifying it.