한테 or 에게 is used when an object belongs to someone. It also means 'to' or 'from'.
But it means something belongs to someone in your sample sentence.
나한테 조금 있어요 literally means "A lttle bit of something belongs to me." So it means "I have a little bit of something."
Here are some more examples.
저한테 돈이 좀 있어요. ( I have some money.)
누구한테 색연필이 있나요? (Who has color pencils?)
You can use '에게' instead of '한테' and '에게' sounds more formal. '한테' is mostly used in speech.
Hope it helps and please follow me at koreanclass.canada on Instagram!