Who owned the HSA? An HSA is only owned by one person, it is not jointly or family owned.
Based on your facts, you are not eligible to contribute any funds to an HSA that you own. Your wife would be eligible contribute up to $5570 to an HSA in her name. (This assumes her Medicare enrollment was really effective August 1 and she was not back-dated as some people are.) Separately, your child is eligible to contribute up to $8550 to an HSA in their name, if she is on your policy and not a dependent. (If she is a dependent, she is not eligible to contribute anything.)
If you contributed $600 to your HSA, that is not eligible, it is subject to a 6% penalty unless you perform a special procedure to remove it, and you don't get a tax deduction. However, your wife is eligible as indicated and could take a tax deduction up to her eligibility limit. You have until April 15, 2025, to remove any excess contributions from your HSA and to make retroactive 2024 contributions to an HSA in your wife's name.
