Only enter the amount you actually paid out-of-pocket.
You don't say for which state you are filing but according to the State of Michigan (and I assume all states that offer the credit):
“Rent Assistance - If any portion of your rent was paid on your behalf by MSHDA, or any other government agency, you are only allowed to claim the portion of your rent that you actually paid. Do not claim any amount that was paid on your behalf by MSHDA or any other government agency.”
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