Is ghusl required if madhy (pre-ejaculate) mixes with yellow discharge, given that the time of its exit is not remembered, the madhy continues to be discharged, and one suffers from Waswas (obsessive doubts)?

"Madhī" is a thin, white fluid that is discharged upon thinking (about sexual matters) or foreplay. It necessitates purifying the body and clothes from it, and performing ablution (wudūʾ) for it. If there is a continuous flow of madhī ( سلس مذي), one must guard with a cloth and perform ablution for each prayer after its time has begun.

As for a woman's "manī" (sexual discharge), it is a thin, yellow fluid with a distinctive odor, discharged with pleasure, and followed by a feeling of languor. If you are uncertain whether the discharge is manī or something else, you may choose and assign it the ruling of one of them.

The normal vaginal discharges of a woman ( رطوبات) are pure and do not require washing, but they nullify ablution according to the majority of scholars. If there is a continuous flow of these discharges ( سلس رطوبات), one must perform ablution for each prayer after its time has begun. Guarding (with a cloth) is not necessary because these discharges are pure. It is advisable to ignore obsessive thoughts (wasāwis).