No, there is not a $500 credit for college students living at home instead of on campus or on their own. There is a $500 Other Dependent Credit that some parents are able to claim when they are not able to claim their college student as a qualifying child anymore (usually because they are over 23 years old).
This would automatically be given to you if you entered your child on your return and answered all the questions regarding your child and then went through the deductions section.
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