Use the Tax Withholding Estimator on the IRS web site to figure out what to put on the W-4 form that you give to your employer. It will show you how to adjust your withholding to get the approximate refund amount that you want.
It's probably too late to make any significant difference for 2023, with only one month left. But you can correct your withholding for 2024. Since you had tax withheld on your previous job in 2023, you might still get a refund, or at least not owe too much.
Make sure tax is withheld on your first paycheck after you give your employer the new W-4. If something is wrong, don't let it go for three months before you do anything about it. The longer the incorrect withholding goes on, the harder it is to correct.
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