I beg your pardon is the correct one.

The British people say it more I think. Keep in mind that the word Pardon, can be used for saying 'sorry' when you have made a mistake or done something wrong. Or it is used to show that you strongly disagree or that you are angry about something that someone has said. For example "I beg your pardon, young man - I don't want to hear you speak like that again!

I beg your pardon is the correct one. Usually this is used when someone said something rude and you want to politely acknowledge your surprise. You can also say, "Pardon me?"

the first one is like when you tell someone sorry And the second one is like when you say I'm sorry. And actually there's no big difference between them .