"갖고" is the short form of "가지고", and both are the same meaning and used in spoken Korean. as for me, "가지고" sounds more common even if short forms are preferred in spoken.

가지고 있어?, 갖고 있어? = Do you have~? If you want to use them like this " Do you have~?" Their meaning are same. You can use both in a conversation.

Ahead of 2 answers are right. so, '가지고 있어? or 갖고 있어?(with question mark and accent on last sound/syllable)' is interrogative sentence. It's question. It means 'Do you have ~ ?' but '가지고 있어 or 갖고 있어(without question mark) is a kind of imperative sentence. it means 'keep holding'