Maran the Rema (98:1) wrote that it is forbidden to kiss one’s small children in the synagogue, in order to firmly establish the love of Hashem (God) in one’s heart and to demonstrate that no love compares to the love of Hashem, may He be blessed.

The author of Shu”t Binyamin Ze’ev (Siman 163), a student of the Maharshal, added that this prohibition applies to one’s adult children as well, not only small children. This also applies in the women’s section (Ezrat Nashim), as the sanctity of the synagogue applies there as well (as explained in Orach Chayim Siman 151). Therefore, Maran the Yechaveh Da’at (Vol. 4, Siman 12) forbade kissing the hands of those called up to the Torah, or a father kissing his son on the day of his Bar Mitzvah.

However, if the kiss is a sign of honor, admiration, or basic etiquette (Derech Eretz), it is permissible. We find this practiced by the Tanna’im (Tannaitic Sages) in various sources, and as Maran the Ben Ish Chai (Parshat Vayikra) elaborates, it is the custom to kiss the hand of a Rabbi. We even find this regarding Moshe Rabbeinu, who kissed Aharon at the Mountain of G-d; this was permitted because it was an act of honor and etiquette toward his older brother.

It should be noted that it is commonly cited in the name of the “Prince of Torah,” Rabbi Moshe Feinstein, that this prohibition applies specifically during the time of prayer.