Will punching by tying a Thera band on my hand or karate belt help me in improving my punching power? I am a karate student of seishinkai shito ryu style.
Fundamentally, no it won't.
A punch is a delivery of kinetic force; a resistance band will simply help you burn more calories and maybe increase your muscle tone a little.
Using a resistance band will tend to work your hand grip, forearms, triceps and anterior deltoid muscles. Punching with weights will do the same however it will also indirectly stress your latissimus dorsi muscles (as they compensate to help you keep balance), you will also tend to adjust the motion so that the medial deltoid muscles also have some assistance.
A resistance band will possibly alter your punch technique in a suboptimal way - the line of resistance will never perfectly line up with the trajectory your punch should take and your muscles will consequently compensate and work in a way that is not an optimal motion for punching, especially once you start to tire. If you really want to apply resistance to your punching movements then do them standing submersed in water.
A resistance band will also not help you build your focus. Focus is that moment when you achieve a combination of maximum tension and maximum kinetic energy and it is a critical element of your punch - if you lack it then the punch is little more than a bludgeon or a shove with a closed fist.
I dont believe it will help with punching power as power relies on mass and speed.
- Mass relies on coordination of the whole body and there is a lot more to be gained practising better coordination.
- Speed relies on coordintaion as well as reducing resistance which is attained by limiting the use of antagonistic muscles. This device will engage them.
What this sort of device can help with is continuous pull power which is better suited to grappling. For example a snap down on a head or arm comes to mind.
I have not tried what you suggest, but it sounds awkward. It also seems to me that it might impede proper form in punch delivery. If you want stronger punches increase the strength of your whole body, focus on using proper form in practice, and do bag work with a partner. Something like a resistance band tied to your belt is going to offer resistance in strange way, and may actually end up doing more harm than good.
If you want some training advice on an exercise that is proven to produce results in your punching speed and strength, start doing Clap Pushups (of course YMMV).