If someone vomits intentionally while fasting, his fast will be broken and he will have to perform qaza. However, if one vomits involuntarily while fasting, the fast will not be broken, and no qaza will be required.
Abu Hurairah (RANarrated by the Messenger of Allah, may Allah bless him and grant him peace, said:
مَنْ ذَرَعَهُ القَيْءُ, فَلَيْسَ عَلَيْهِ قَضَاءٌ, وَمَنْ اسْتَقَاءَ عَمْدًا فَلْيَقْض.
Meaning: If someone vomits involuntarily, he does not have to perform his qaza. A person who intentionally vomits should perform Qaza (i.e. his fast will be broken). (Sunan at-Tirmidhi: 720)
It should be noted that many people have the wrong idea that if they vomit while fasting, the fast will be broken and they will have to perform Qaza. If the fast is thought to be broken after involuntary vomiting after involuntary vomiting, then the fast will be broken and Qaza will be wajib, kaffarah will not be wajib