What are the Athkaar to be recited to protect others against my evil eye and that will protect me against theirs?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Sahl ibn Hunayf narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said that anyone who admires something in his brother should supplicate Allaah The Almighty to bless it. [Ahmad and Al-Haakim]

‘Aamir ibn Rabee‘ah narrated that  the Prophet, sallallaahu ‘alayhi wa sallam, advised anyone who saw what he considered pleasing about himself, what he or a fellow Muslim possesses, he should ask Allaah The Almighty to bless it, for the effect of the evil eye is  a fact. [An-Nasaa'i: ‘A‘maal Al-Yawm Wal-Laylah. Al-Haakim. (Al-Haakim and Al-Albaani: Saheeh)]

In addition, Allaah The Almighty Says (what means): {And why did you, when you entered your garden, not say, 'What Allaah willed [has occurred]; there is no power except in Allaah.} [Quran 18:39]

Some of the righteous predecessors mentioned that anyone who admired anything about himself, his property or his children should say, "Ma Shaa’a Allaah La Quwwata Illa Billaah" (What Allaah Willed [has occurred]; there is no power except in Allaah). These words are based on this verse.

According to a Hadeeth narrated by Anas the Prophet, sallallaahu ‘alayhi wa sallam, said that anyone who has been blessed with something from Allaah The Almighty either in his property, family or children and said , "Ma Shaa’a Allaah La Quwwata Illa Billaah", this blessing would be protected from any affliction except death. [Abu Ya‘laa: Al-Musnad. Al-Bayhaqi: Shu‘ab Al-’Eemaan]

Moreover, the Prophet, sallallaahu ‘alayhi wa sallam, ordered a man who liked something about his fellow Muslim to ask Allaah The Almighty to bless him. He added that the evil eye might  harm a person until it caused his death. [Ahmad, An-Nasaa'i and Ibn Maajah. (Al-Albaani: Saheeh)]

The aforementioned are the supplications to be said when a Muslim sees anything that appeals to him and fears that he may affect it with his evil eye.

On the other hand, one can protect oneself from the evil eye once he observes the following. ‘Aa’ishah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, ordered to seek refuge in Allaah The Almighty from the evil eye, and he added that the harmful effect of the evil eye is a fact.  [Ibn Maajah. (Al-Albaani: Saheeh)]

Abu Sa‘eed Al-Khudri narrated on the authority of the Prophet, sallallaahu ‘alayhi wa sallam, that he used to seek refuge in Allaah The Almighty from the evil eye of the Jinn,  then the evil eye of the humans . After the two chapters of Al-Falaq and An-Naas had been revealed, he switched to reciting them for the same purpose. [At-Tirmithi and Ibn Maajah. (At-Tirmithi: Hasan)]

Therefore, reciting these two Chapters after prayer protects against the evil eye.

Allaah Knows best.