Question about taxes on second job...

The state should have a form equivalent to the W4 (Louisiana has the L4) where you provide your status (single/married) as well as dependents and extra withholdings. You should update that form and increase your extra withholdings.

If they are aware that this is your 2nd job, they usually take out more taxes on the suspicion that you would be in a different bracket than their base pay suggests.

That said, you should be able to make adjustments (unless it is commissionable or bonus income).

Edit to add: tell your primary employer of the 2nd income source and they may deduct at a different formula also.

I just withhold more at my primary job to cover investment income throughout the year and some other side job income I get as well as my wife gets. On my W-4 for federal and G-4 for GA I just fill in flat amount extra to be taken each paycheck.

This year between my wife and I we owe about $400 to federal and getting $800 back from state so consider that mostly a success