In the Quran there is mention of the fast of Maryam عليه السلام:
إني نذرت للرحمن صوما فلن أكلم اليوم إنسيا
Verily! I have vowed a fast unto the Most Beneficent (Allah) so I shall not speak to any human being this day.
— Quran 19:26
والمراد أنهم كانوا إذا صاموا في شريعتهم يحرم عليهم الطعام والكلام ، نص على ذلك السدي ، وقتادة ، وعبد الرحمن بن زيد
The meaning here is that in their Law, when fasting, it was forbidden for them to eat and speak. As-Suddi, Qatadah and `Abdur-Rahman bin Zayd have all stated this view.
— Tafsir Ibn Kathir [English translation]
In hadith there is mention that they did not take suhoor and that they delayed iftar:
فصل ما بين صيامنا وصيام أهل الكتاب أكلة السحر
The difference between our fasting and that of the people of the Book is eating shortly before dawn.
لا يزال الدين ظاهراً ما عجل الناس الفطر لأن اليهود والنصارى يؤخرون
Religion will continue to prevail as long as people hasten to break the fast, because the Jews and the Christians delay doing so.
— Abu Daud
In one variant of a hadith, there is a claim made by the Jews that the fast of Ashura was kept by Musa عليه السلام:
فقالوا هذا يوم عظيم وهو يوم نجى الله فيه موسى وأغرق آل فرعون فصام موسى شكرا لله فقال أنا أولى بموسى منهم فصامه وأمر بصيامه
They used to say: "This is a great day on which Allah saved Moses and drowned the folk of Pharaoh. Moses observed the fast on this day, as a sign of gratitude to Allah." The Prophet (ﷺ) said, "I am closer to Moses than they." So, he observed the fast (on that day) and ordered the Muslims to fast on it.