"Admonish" means to warn or reprimand someone firmly, often in a mild manner.
The word "reprove" is a synonym, as it also means to criticize or correct someone, typically for behavior or actions that are deemed inappropriate.
"Spurn" (1) means to reject or disdain, which is not related to offering a mild reprimand or warning.
"Manikin" (2) refers to a small model of the human body or a figure used for display, unrelated to criticism or admonition.
"Quell" (4) means to suppress or put an end to something, which is not the same as offering a reprimand or advice.
Conclusion:
"Reprove" is the correct synonym for "admonish," as both involve giving a firm but constructive correction or reprimand.