What is the ruling on doubting the emission of semen while fasting due to waswas (obsessive whispering), and is it necessary to re-fast only that day, or that day along with expiation, knowing that the doubtful secretions were discovered after breaking the fast?

The cure for obsessive thoughts is to disregard them and not pay attention to them. Your fast is valid according to the Maliki school, and you are not required to make up the fast or offer expiation. The secretions mentioned are vaginal moisture (rutubat al-farj) and do not invalidate the fast; rather, they nullify ablution (wudu'). The female semen (maniyy al-mar'ah) is thin and yellow, discharged with desire, followed by a sensation of fatigue, and has a distinctive odor. If you are unsure whether the discharge is semen or something else, choose one of the rulings and attribute it to the discharge. This is more lenient for you due to your affliction with obsessive thoughts. Vaginal moisture (rutubat al-farj) nullifies ablution (wudu'). You are not required to make up previous prayers because the original assumption is that the discharge occurred later. Disregarding obsessive thoughts is what jurists prescribe as a cure for them.