„Have got” is used in British English

„Have” is used in American English 

Both versions are correct and can be used to express posession in English.

U.K. – I have got a laptop, I will bring it.

U.S. – I have a red car and my husband has a black one.

The verb „have got” only has a present form (NOT past tenses).

U.K. – I had a laptop.

U.S. – I had a red car and my husband had a black one.

 Have got – use

Possession, family

She‘s got a nice apartment.

Have you got a computer?

I haven’t got any brothers or sisters.

Illnesses

I‘ve got a headache.

She‘s got a cold.

Physical descriptions

He‘s got brown hair and a long nose.

They‘ve got blue eyes.