When will I get the rest of my refund? Turbo tax only deposited $502 of my federal refund.

TurboTax does not receive any kind of tax refund, federal or state.

See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

Why is my refund different than the amount on the tax return I filed? 

All or part of your refund may have been used (offset) to pay off past-due federal tax, state income tax, state unemployment compensation debts, child support, spousal support, or other federal nontax debts, such as student loans. To find out if you may have an offset or if you have questions about an offset, contact the agency to which you owe the debt.

We also may have changed your refund amount because we made changes to your tax return. This may include corrections to any incorrect Recovery Rebate Credit amount. You’ll get a notice explaining the changes. Where’s My Refund? will reflect the reasons for the refund offset when it relates to a change in your tax return.

Tax Topic 203, Refund Offsets for Unpaid Child Support, Certain Federal and State Debts, and Unemployment Compensation Debts has more information about refund offsets.

TT does not receive tax refunds, so could not have deposited it.   The IRS will be mailing you a letter about the adjustment and/or offset that they made. They do not notify TT.

How much is missing?  Federal and state come separately.  A common adjustment is if you claimed the Recovery rebate credit on 1040 line 30 when you already got the Stimulus payment or got the second one after you filed or reported the wrong amounts or entered the wrong amounts in the 2 boxes.  If you entered the total you got for both rounds in the same box it would think you didn't get the other one.