The Prophet ﷺ said, "Whoever is overcome by vomiting is not required to make up the fast, but whoever induces vomiting must make it up."
حدثنا عبيد الله بن عبد الكريم حدثنا الحكم بن موسى حدثنا عيسى بن يونس ح و حدثنا عبيد الله حدثنا علي بن الحسن بن سليمان أبو الشعثاء حدثنا حفص بن غياث جميعا عن هشام عن ابن سيرين
عن النبي ﷺ قال من ذرعه القيء فلا قضاء عليه ومن استقاء فعليه القضاء
[Its chain of transmission is daif] Abu Dawud narrated it in the Book of Fasting, chapter on the fasting person who deliberately induces vomiting, hadith no. 2380, through the narration of Isa bin Yunus, and Tirmidhi graded it hasan, hadith no. 720. Ibn Khuzayma, Ibn Hibban, Hakim, and Dhahabi graded it sahih, while Bukhari graded it daif.Hisham bin Hassan is a mudallis, described as such by Ibn Madini and others (third tier of the mudallisin), and I did not find an explicit statement that he heard it directly. It has several paths of transmission, all of them daif.