The Messenger of Allah ﷺ said, "Whoever is overcome by vomiting is not required to make up the fast, but whoever induces vomiting must make it up."
حدثنا الحكم قال عبد الله وسمعته أنا من الحكم بن موسى حدثنا عيسى بن يونس حدثنا هشام بن حسان عن محمد بن سيرين
قال رسول الله ﷺ من ذرعه القيء فليس عليه قضاء ومن استقاء فليقض
Its isnad is sahih. Abu Dawud narrated it, 2/310, no. 2380, in the Book of Fasting, chapter on one who fasts and vomits deliberately, and Tirmidhi, 3/79, no. 720, and he said, hasan gharib. And Ibn Majah, 1/536, no. 1676.