During the month of Ramadan, I ate dates a few minutes before the Athaan (call to prayer) of Fajr and then fell asleep. I woke up when the Iqaamah (immediate call to prayer) was being pronounced with a relatively large piece of date in my mouth. Its taste mixed strongly with my saliva and I felt it in my palate. Was my fasting valid on that day or is anything due on me? May Allah reward you.
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The questioner did not mention whether or not he swallowed that piece of date. However, it appears from the question that he swallowed the saliva which mixed with the taste of dates, and that he did so unintentionally during sleep or when he woke up. In both cases, his fast is nonetheless valid.
Ibn Qudaamah said in his "Al-Mughni", "Waking up in the morning with food between the teeth can be of two types: the first is that the food particle might be too small to be spat out and therefore is swallowed: in this case the fast is not broken because such swallowing is unavoidable since that food particle has become similar to the saliva in the mouth...” Ibn Al-Munthir comments on this saying, "Scholars have consensus on this."
Ibn Qudaamah continues, “The second is that the food particle may be big. If it is spat out, the fast is valid, but if swallowed intentionally, the fast will be invalid according to the majority of scholars."
The same ruling applies if the taste mixes with the saliva of the mouth. Ibn Qudaamah said about committing a fast-breaking act during sleep, "And if one does any act that would break his fast during sleep, then his fast would not be invalid because the act is not intentional nor is the person aware of his state of fasting, which makes it even more excusable than breaking one’s fast forgetfully."
Allah Knows best.