Literally 4 different ones exist: Eggnog, Ajerkoniak, Rompope, Advocaat

(though none use fermented eggs, it’s a liqueur of spirit + egg + spice, that makes an alcoholic custard)

Also, egg white is often used in cocktails, whisked with simple syrup, to make a foam, such as in a Whisky Sour

Eggnog?

In my fridge. I make some every year.