After a modal verb you can only use one of the four infinitive forms: simple, continuous, perfect or perfect continuous. He might be a magician. She could go to party. She should be studying now. I will be waiting when you arrive. He must have gone home early. She might have been a spy. It must have been raining when he went for a walk. She might have been waiting for someone. The simple and continuous infinitives tell us about the present and the future. The perfect and perfect continuous infinitives tell us about the past. These could describe past simple, past continuous, present and past perfect, and present and past perfect continuous situations. It is important to remember that only one of four forms is possible after a modal verb.

should have :) 'should had' doesn't exist

She should have studied. You have to use such tenses after a modal verb.

‘ She should have studied harder for the exam’ The adverb ‘harder’ should accompany the verb to which it refers i.e. studied. In British English it is more usual to talk about ‘working hard’ than ‘studying hard’.

Have