Adding 'got' to the verb 'to have' is not proper and is more of a slang term added for no extra effect. I can say 'I have an apple' and say 'I have got an apple' and it means exactly the same thing. Got should be used as past tense for 'get' instead. 'I got an apple yesterday' is correct. If you got the difference then have done my job here. :)

They can both mean possession, or obligation (have to / have got to), but in a regular sentence, you contract "have" when you use "have got". Correct: I have two legs from my hips to the ground. I've got two legs from my hips to the ground. Incorrect (or simply unnatural): I have got two legs from my hips to the ground. I've two legs from my hips to the ground. When it's a question, the auxiliary (helping) verb is different, but the meaning is the same. I have... / I don't have... / Do you have...? / Yes, I do. No I don't. (auxiliary verb: do) I've got... / I haven't got... / Have you got...? / Yes, I have. No, I haven't. (auxiliary verb: have)

I agree with Andy's answer.