This hadith has been narrated on the authority of Ayyub with the same chain of transmitters.
Sahih Muslim Book 13, Hadith 165
← Previous Hadith What is the (significance) of this day that you observe fast on it? They said: It is the day of great (significance) when Allah delivered Moses and his people, and drowned the Pharaoh and his people, and Moses observed fast out of gratitude and we also observe it. Upon this the Messenger of Allah (ﷺ) said: We have more right, and we have a closer connection with Moses than you have; so Allah's Messenger (ﷺ) observed fast (on the day of 'Ashura), and gave orders that it should be observed.

Sahih Muslim Book 13, Hadith 164 Next Hadith → The day of 'Ashura was one which the Jews respected and they treated it as Id. The Messenger of Allah (ﷺ) said: You also observe fast on this day.

Sahih Muslim Book 13, Hadith 166