Abu Hurairah reported, and I only know that he traced the hadith back to the Messenger of Allah ﷺ, that he said, "Responding to a Muslim's sneeze with the supplication is done three times. If he sneezes more than that, then it is a cold."
عن أبي هريرة، لا أعلم إلا أنه رفع الحديث إلى رسول الله ﷺ أنه قال: تشميت المسلم إذا عطس ثلاث مرات، فإن عطس فهو زكام.
No references are available.
Abu Dawud (5035) narrated it, and Ibn Sunni in Amal al-Yawm wal-Layla (251) both narrated it from the hadith of Isa bin Hammad Zughba, who said, Layth bin Saad informed us, from Muhammad bin Ajlan, from Saeed bin Abu Saeed Maqburi, from Abu Hurairah, I do not know except that he traced the hadith up to the Messenger of Allah ﷺ, that he said... and he mentioned it. Then Abu Dawud said after it, "Abu Naeem narrated it, from Musa bin Qays, from Muhammad bin Ajlan, from Saeed, from Abu Hurairah, from the Prophet ﷺ." Its chain is hasan because of Muhammad bin Ajlan, for his hadith is hasan.There has been disagreement over whether Muhammad bin Ajlan traced it up as a raised hadith. Ibn Abu Hatim asked his father, saying, "Who traces it up, and which of the two is more sahih?" He said, "A group of reliable narrators trace it up." Abu Hatim's answer suggests that tracing it up is the preserved version. However, Daraqutni held the view that the stopped version was more likely. See Ilal Ibn Abu Hatim (2376) and Ilal Daraqutni (2054).On this subject there is also what was narrated from Ubayd bin Rifa Zurqi, from the Prophet ﷺ, "The one who sneezes is to be blessed three times, and if he sneezes more than that, then bless him if you wish, or not, if you wish." Abu Dawud (5036) narrated it through Malik bin Ismail, who said, Abdul-Salam bin Harb told us, from Yazid bin Abdul-Rahman, from Yahya bin Ishaq bin Abdullah bin Abu Talha, from his mother, Humaydah or Ubayda bint Ubayd bin Rifa Zurqi, from her father, and he mentioned something similar.Tirmidhi (2744) narrated it through Ishaq bin Mansur Saluli Kufi, from Abdul-Salam bin Harb, from Yazid bin Abdul-Rahman Abu Khalid, from Umar bin Ishaq bin Abu Talha, from his mother, from her father, and he mentioned it. This is his wording. Tirmidhi said, "This is a gharib hadith, and its chain is unknown."Tirmidhi's statement that its chain is unknown refers to Umar bin Ishaq and his mother. As for Umar bin Ishaq, the correct name is Yahya bin Ishaq, as it appears in Abu Dawud's version, and he is a well known reliable narrator. So the defect is confined to his mother, Humaydah, and as Tirmidhi said, no one but Ibn Hibban has affirmed her reliability. As for Ubayd bin Rifa Zurqi, he was born during the era of the Prophet ﷺ, and his hadith is counted among the mursal reports of the companions.