TMAs contain a number of hand strikes outside of punches and backfists. These include the:
- Palm heel
- Arc hand
- Two-finger poke
- Bow wrist
- Index knuckle (as seen in Choong-Jang) 
- Middle knuckle
The latter shows up in Gae-Baek, Choi-Yong, So-San, and the KTA poomsae Cheonkwon. It is performed either straight out or upwards like an uppercut.
|Middle knuckle strikes from Gae-Baek (left), Choi-Yong (middle), and Cheonkwon (right)|
|(Left): American Kempo-ist demonstrating middle knuckle strike to armpit. Source: casadekenpo (Right) Vital point diagram from The Encyclopedia of Taekwon-Do.|
What about the straight knuckle punch in Choi-Yong? Here I don't prefer the philtrum as a target because while it may push away the opponent, is it unlikely to end the fight. We can use the previous movement in the form -- cat stance forearm guarding block -- as an armlock to turn the opponent. This exposes the side of their neck for a knuckle fist strike.
|David Gimberline demonstrating a strike to the side of the neck. Source: Shuhari Institute|
 The twin index knuckle fist in Choong-Jang is aimed at the opponent's temples. Presumably the index knuckle gives you more motor control to dig in.