Q.  Can the taxes paid from wage garnishment be included (added) to taxes paid from withholding?

A. No.  Federal income tax paid for past years is not deductible and is not reported on the current year federal tax return.

State income tax paid for past years is deductible, on the federal return; but only for taxpayers who itemized deductions. 

it depends on who is taking your money, the IRS or your State.

I paid IRS wage garnishments in 2020. Is this considered taxes paid for the tax year? These are taxes paid via wage garnishment, but not sure if they are taxes paid for purposes of 2020 tax return?  It is an IRS wage garnishment (not state).  

Wage garnishments, by the IRS, are for past year's unpaid income tax. As such, they are not entered anywhere on your 2020 tax return. 

There are six states that allow you to enter the federal tax you paid on your state return--Alabama, Iowa. Louisiana, Missouri, Montana, and Oregon.  If you are filing in one of these states watch for the deduction when you prepare your state return.