Hey, Leila! The second one is correct! :) Examples: https://dictionary.cambridge.org/grammar/british-grammar/have-got-and-have Have a good day! :)

2nd

Neiher. The second is common and coloquial but ungrammatical. I always recommend that adult learners stay away from contractions.

I've got it is correct . You can't use have get because get is present tense. I get it. I think it is fine to use contractions because native speakers use them all of the time. This is an informal form. Who has the newspaper? I can't find it anywhere. I've got it or I have it.

"I've got it" is correct. "Have" and "get" do not go together. You could have "I'll get it", but it has a very different meaning.