I need constructor or init function that can be run for my custom module. I need to call it every time when request made to my module's controller in magento.
Magento already has this. You can use
_construct if you want your logic when the controller is instantiated or you can use
preDispatch that is called when an action is called.
Just make sure that your controller extends
Mage_Core_Controller_Front_Action if it's a frontend controller or
Mage_Adminhtml_Controller_Action if it's an admin controller.