Ishould have studied more. i should of study more. which one is the correct sentence?

I should have studied more is the correct sentence.

Should have is a modal verb used to talk about something hypothetically, an action that didn't really happen. Should have + past participle expresses a regret; something that was supposed to happen, ot that should have happened, but didn't.

"Should of" does not exist in correct English grammar.

I should have studied more. This is the correct sentence.

The speaker is expressing a regret; now it is too late to change the result of a past action / decision. The speaker is referring to the  past; he / she did not study enough ,probably, for a test and he / she could not have passed the exam or could have got a low grade. Now, at the moment of the message, the speaker thinks that if he/ she had studied more, he / she would have got a different result. Therefore, the speaker regrets, now, not having studied enough. This regret over his / her past actions is expressed with " should " + " perfect infinitive".

- I should of study more. ( This option is wrong. The prepositon " of" never follows a modal verb  and the verb " study" is in the infinitive).