What is the ruling on the fast of one who sniffs up mucus and it goes down their throat against their will? Is that considered intentional swallowing? What is the preferred ruling on intentionally swallowing mucus? Is a fasting person obliged to try to expel mucus or phlegm from their throat if they feel it?

The scenario described does not involve intentionally swallowing mucus, but rather intentionally drawing it into the mouth, not for the purpose of swallowing it. Intending to do so does not invalidate the fast, similar to rinsing the mouth. If one then swallows it unintentionally, the fast is not broken, for unintentionally swallowing mucus does not invalidate the fast. For the differing opinions on breaking the fast by swallowing phlegm, and the ruling on attempting to expel mucus, relevant fatwas can be consulted.