If your 23 year old child and their child (your grandchild) both live in your home, you can probably claim both of them as dependents.
As stated, someone who is claimed as a dependent can't have dependents of their own, and since your adult child has no income, they won't receive any credits or refund even if they claimed their own child.
Also note that,
1. Your 23 year old can be your qualifying child dependent if they are a full time student and live in your home (or are temporarily living at college but considered to live at home). If they do not live in your home but you pay more than half their living expenses, or if they live in your home but are not a student, they can be a qualifying relative dependent. Both types of dependent allow you to claim a $500 credit only.
2. Your grandchild can be your qualifying child dependent if they live in your home more than half the year (or more than half the days since they were born if they were born in 2023). This is worth up to $2000 child tax credit depending on your other tax facts. If they do not live in your home but you pay more than half their living expenses, they are a qualifying relative dependent for a $500 credit.
