If you are a sole-proprietor (your income is reported on Schedule C for the Federal Return), you will pay estimated Federral taxes quarterly using Forms 1040-ES. There is also a worksheet to help you to keep track of your payments.
For Kentucky, you will use Forms 740-ES. They are very similar to the Federal Forms, but they are for KY estimated quarterly payments. These forms also come with a worksheet to help you keep track of your payments.
Both the Federal as well as KY estimated payments are due on 4/15, 6/15, 9/15, and 1/15 (of 2020). If the 15th of any of those months falls on a weekend or holiday, the payment is due to be mailed on the next business day open (usually the following Monday).
For information on how to set up estimated payments in TurboTax, please see this FAQ (the link is for Federal estimates, but there is a link inside for the state estimates also): https://ttlc.intuit.com/replies/4242911
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