If you work remotely in Texas for your own convenience, you will owe NY taxes.

If your work is for the necessity of the employer, rather than convenience, you should not be subject to NY state income taxes.

To be exempt from New York taxation, such wages must entail “duties … which by their very nature, cannot be performed at the employer’s place of business."

If you had any NY state workdays, you will be taxable on days you worked in NY.

Please see the following link for NY treatment of nonresidents and part-year residents and the convenience of the employer test  .  https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf

If you are working in Texas because that is the only place you can perform your work, you can file a nonresident NY return for taxes erroneously withheld.