Ideally your employer should withhold your IN tax. If they don't, you must make quarterly estimated tax payments to IN. See this reference for more details:
https://www.in.gov/dor/individual-income-taxes/payments-and-billing/estimated-tax/
Because of reciprocity, residents of IN who work in KY are not subject to KY income tax on their W2 earnings. But their income is fully taxable by their resident state of IN.
If you haven't already done so, you should file KY Form 42A809 with your employer, so that they don't withhold KY taxes from your pay. Here's a link to that form:
https://revenue.ky.gov/Forms/42A809.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
