This reference details New York's criteria for determining if an out-of-state workplace is a "bona-fide office":
https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
If your workplace in Texas satisfies those criteria, and you're working there as an employment requirement, then the income you earn there is not subject to NY taxation.
Income you earn by (physically) working inside New York is subject to NY taxation. So you should keep track of those days.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
