strictness, severity, rigidity
嚴 centers on imposing firm control: strictness, severity, or rigidity in rules or demeanor.
嚴 is the traditional form of 厳. It combines 吅 (two mouths, suggesting a commanding voice) with 敢 (daring) under 厂 (cliff), conveying an imposing, strict authority. The modern simplified form 厳 replaces the top with a different element.
Two mouths 吅 shouting commands from a cliff 厂 with a daring 敢 attitude: that is strictness and severity.
For ゲン, imagine a strict general barking orders: general -> ゲン, and his severity echoes from the cliff.