Imam Shafi’i, may Allah have mercy on him, said: Whoever vomits intentionally while fasting, it is obligatory upon him to make up the fast. And whoever vomits unintentionally (i.e., does not do so deliberately), then making up the fast is not obligatory upon him.
Hadith Referenceمسند الإمام الشافعي / كتاب الصيام / 658
Hadith Takhrijاسناده صحیح اخرجه البيهقى 219/4 ۔ وفى المعرفة السنن والآثار له ، رقم : (2475)