Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
Qurʾān Bukhārī Muslim Nasāʾī Abū Dāwūd Tirmidhī Ibn Mājah Mālik Aḥmad Dārimī Ḥākim Ibn Ḥibbān Ṭabarānī Nasāʾī's Kubrá Bayhaqī al-Luʾluʾ wa-al-Marjān Ibn Rajab's Fifty Riyāḍ al-Ṣāliḥīn Aḥmad's Zuhd Suyūṭī
suyuti:4705a –
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السيوطي:٤٧٠٥a –

"إِنَّ اللهَ تَعَالى افْترَضَ صَوْمَ رَمَضَانَ، وَسَننْتُ قِيَامَهُ، فَمَنْ صَامَه إِيمانًا وَاحْتِسَابًا وَيَقِينًا كَانَ كَفَّارةٌ لِمَا مَضى".  

[هب] البيهقى في شعب الإيمان عن عبد الرحمن بن عوف

See similar narrations below:

Collected by Suyūṭī
suyuti:4888a –
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السيوطي:٤٨٨٨a –

"إِنَّ الله تَعَالى فَرَضَ صِيَام رَمَضانَ، وَسننتُ لَكُمْ قِيامه فَمَن صَامه وَقَامَه إِيمانًا واحْتسَابًا خَرَجَ مِن ذُنوبه كيوْم وَلدَتْهُ أُمُّهُ".  

[حم] أحمد [ن] النسائي عن عبد الرحمن بن عَوْف