The Prophet ﷺ said: if one has a sudden attack of vomiting while one is fasting, no atonement is required of him, but if he vomits intentionally he must make atonement. (Using translation from Abū Dāʾūd 2380)
أَنْ يَقْضِيَ وَإِنْ كَانَ ذَرَعَهُ الْقَيْءُ وَهُوَ صَائِمٌ فَلَيْسَ عَلَيْهِ الْقَضَاءُ»
The Prophet ﷺ said: if one has a sudden attack of vomiting while one is fasting, no atonement is required of him, but if he vomits intentionally he must make atonement.
قَالَ رَسُولُ اللَّهِ ﷺ مَنْ ذَرَعَهُ قَىْءٌ وَهُوَ صَائِمٌ فَلَيْسَ عَلَيْهِ قَضَاءٌ وَإِنِ اسْتَقَاءَ فَلْيَقْضِ
Yahya related to me from Malik from Nafi that Abdullah ibn Umar used to say, "If some one makes himself vomit while he is fasting he has to make up a day, but if he cannot help vomiting he does not have to make up anything."
أَنَّهُ كَانَ يَقُولُ مَنِ اسْتَقَاءَ وَهُوَ صَائِمٌ فَعَلَيْهِ الْقَضَاءُ وَمَنْ ذَرَعَهُ الْقَىْءُ فَلَيْسَ عَلَيْهِ الْقَضَاءُ
"مَنْ ذَرَعَهُ القَيْيُ وَهُوَ صَائِم فَلَيسَ عَلَيهِ قَضَاءٌ، وَمَنْ اسْتَقَاءَ عَمْدًا فَليَقْضِ".