I was pregnant while living with my parents, i moved in October and had my child in December can my parents claim my child because they’re claiming me

[DoninGA]

A dependent cannot claim anyone else as a dependent.

[Opus 17]

Probably yes.

Your parents can claim your child (their grandchild) as a dependent if the child lived in their home more than half the year since being born, and if your parents' taxable income is higher than yours.  (For the "lived with" question, your parents select "all year", which is the correct answer for a newborn.) 

If your taxable income is higher than your parents, then only you can claim the child--but you can't claim a dependent if you are someone else's dependent, so your parents would have to not claim you.  (It would be an unusual combination of financial circumstances where you had a higher income than your parents but they were still entitled to claim you as a dependent.)