Is the fast of one who spat out a morsel from his mouth at the time of the Adhan, and swallowed his saliva which contained the taste of food, acceptable?

Your fast is valid as long as you spit out the food from your mouth upon hearing the Adhan (definition). Swallowing saliva mixed with a tiny bit of food does not affect the fast if it is difficult to avoid, or if you did not intend to swallow it. So, whoever wakes up with food in their mouth and spits it out, their fast is not broken, by consensus. Similarly, if it is difficult to spit it out and one swallows it with their saliva unintentionally, or if their saliva mixes with a food remnant that is impossible to spit out, or if one habitually swallows their saliva, their fast is not broken.