Thank you for your question.
If you live and work in MO, then the NY Company should be withholding for MO. BUT the NY office may not have a NEXUS in MO and may not know how to deal with that. So they may end up withholding for NY.
Contact your payroll and find out how they are doing it.
if they withhold for NY you will have to file a NY non-resident return to get any refund, and then file a MO resident return. MO would give you credit for any taxes paid to NY.