They mean the same thing. The second one is not correct, but people do use it in speaking even though it is strictly speaking incorrect. I would say the first one is best to use when speaking and the third one in writing.
"I got a sister." is incorrect English but it is commonly used among uneducated individuals. "I have a sister." is correct English grammar. "I've got a sister." is incorrect grammar, but then again it is common speech. "I've" is contraction of "I have", so saying "I've got a sister." is saying "I have got a sister." You will never hear "I've a sister." but you will hear "I have a sister." However, depending on the dialect and region, British or American, it will sound like "I've a sister."
I hope this helps. Native English speakers tend to speak English incorrectly. American English can be even more confusing as the various amounts of culture tend to mix in with English producing varying amounts of dialects.