Narrated Abu Burdah: The Jews used to try to sneezes in the presence of the Prophet ﷺ hoping that he would say to them: "Allah have mercy on you!" but he would say: May Allah guide you and grant you well-being!
Hadith Referenceسنن ابي داود / كتاب الأدب / 5038
Hadith Gradingالألبانی:صحيح | زبیر علی زئی:إسناده صحيح, مشكوة المصابيح (4740), أخرجه الترمذي (2739 وسنده صحيح) سفيان الثوري صرح بالسماع عند الحاكم (4/268)
Hadith Takhrij« سنن الترمذی/الأدب 3 (2739)، (تحفة الأشراف: 9082)، وقد أخرجہ: مسند احمد (4/400، 411) (صحیح) »
Benefits and Issues: To a non-Muslim, in response to his sneeze, instead of saying (yarhamuk Allah), one should say (yahdikum Allah wa yuslih balakum), just as one cannot initiate (as-salamu alaykum) to him. And if he says it, then in reply only "alaykum" is said.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 5038
´Narrated Abu Musa:` The Jews used to sneeze in the presence of the Prophet (ﷺ) hoping that he would say: 'Yarhamukumullah (May Allah have mercy upon you).' So he said: 'Yahdikumullahu Wa Yuslihu Balakum (May Allah guide you and rectify your affairs).'"
Shaykh Dr. Abdur Rahman Freywai
Explanation: 1: From this hadith, it is understood that in response to the sneeze of non-Muslims, only (yahdikumullahu wa yuslihu balakum) should be said. And (yarhamukumullah) ("may Allah have mercy on you") should not be said, because the mercy of Allah in the Hereafter is exclusively for Muslims.
Source: Sunan al-Tirmidhi – Majlis ‘Ilmi Dar al-Da‘wah, New Delhi Edition, Page: 2739