Can I still have a period if I’m pregnant?

Dear Doctor, After all the classic symptoms of pregnancy, I took a test and it came out positive. I’m 24 years old and this is my first. I’m not sure how far along I am though. However, for about three days now, I’ve had what I assume is a period. Is that possible? Can I still get my period even when pregnant. I’ve heard people talk about spotting during pregnancy, should I be worried?
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Dr. Rachna Pande