##Limestone caves##
Limestone caves
Build your fortress in a region already full of caves and passages. Limestone is absolutely ideal for this, since it naturally forms all kinds of caves and other strange structures. Case in point - the Tsingy de Bemaraha in Madagascar.
You would conceal the entrances to your fortress in existing, natural caves, and yes, that's 'entrances', plural. If you have a single Great Gate, the enemy can locate it and besiege it. Instead, you'd have a main gate, then several smaller passages leading to outlets all over the mountain. That would allow your forces to sally forth during a siege and harass the enemy's rear and supply lines.
Ultimately, the mountain itself is your best defense. It's difficult to campaign in the mountains, and defenders always have an advantage anyway.