A very formal, literary honorific term for addressing or referring to someone's father. Extremely rare in modern spoken Japanese; more common in classical or highly formal written contexts.
In the letter, it was written, 'Please give my regards to your father.'
Compound of 厳 (gen, 'strict, severe') and 君 (kun, 'lord, master'). The exact historical derivation is uncertain; the spelling is conventionally associated with a respectful term for one's father.