The Prophet ﷺ used to touch the Yamani corner but did not touch the other two.
حدثنا عبد الرزاق أخبرنا معمر عن الزهري عن سالم
أن النبي ﷺ كان يستلم الركن اليماني ولا يستلم الآخرين
Its isnad is sahih. This narration mentions touching the Yemeni corner, while leaving the other one unmentioned, meaning the Black Stone, because its meaning is obvious, as indicated by his statement afterward, "and he did not touch the other two." Bukhari (3:379), Muslim (1:360), and Abu Dawud (2:114) narrated through Layth, from Zuhri, from Salim, from his father, "I never saw the Prophet ﷺ touch anything of the House except the two Yemeni corners." Munziri attributed it to Nasai and Ibn Majah as well. The meaning of this has already passed within a hadith narrated by Ubayd bin Jurayj from Ibn Umar, 4672, 5338.