Is the fast of one who woke up ten minutes after the Fajr Adhan and intended to fast after waking up accepted, knowing that he had been asleep since Asr?

"Tabyit al-niyyah" (forming the intention overnight) for an obligatory fast is a condition for its validity according to the majority of scholars.

The majority of scholars differed regarding the Ramadan fast: is one intention at the beginning of the month sufficient, or is an independent intention, formed overnight, required for each day? The Shafi'is, Hanafis, Ibn al-Mundhir, and the well-known narration from Ahmad said: An intention is required for each day, formed during the night. The Malikis, Ishaq, and the second narration from Ahmad said: One intention is sufficient for the entire month if one intends to fast all of it. This is what Ibn 'Uthaymeen preferred, provided that the fast is not interrupted by breaking it for an excuse.

Conclusion: There is a difference of opinion regarding the validity of your fast. The more cautious approach is to make up this day. However, if you act upon the other opinion, that is permissible for you, as it is a strong opinion. Your abstention from eating and drinking on that day was obligatory due to the sanctity of the time.