Honestly, I'm not sure.
This could be something that varies by state. The last year I was independent I got fined for not making quarterly payments. I've not done more independent work to know exactly how.
Personally only have experience with paying taxes after a year and not doing the quarterly payments. I was paid $20/hour, worked about 25 hours a week. I figured I could save enough money come next April instead of sending checks every quarter.
Once I filed I had to owe taxes (as expected) but don't remember being charged a fine for not paying quarterly. The job was in 2017. Not sure if the rules have changed though.
Depending on the amount you owed they may require you to make quarterly estimated payments the next year -- regardless of what you expect to make. You can counter that with some other IRS forms though.
In particular there is one you can file that basically says I have no idea how my money will come in and can't possibly pay 1/4 of it in Q1. This can help avoid any future fines where the IRS will penalize you saying you withheld payment till the end of the year.
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