If you are an employee under what's called "common law" then you must receive a W-2 for all compensation provided to you in return for your services. The only time it is acceptable to get a 1099-NEC and a W-2 from the same employer is if your relationship actually changed during the year, from independent contractor to employee. Whether you have an employee or independent contractor relationship depends on who controls the time, manner and place of your work.
https://www.irs.gov/businesses/small-businesses-self-employed/independent-contractor-self-employed-o...
If you always had an employee relationship, your employer is breaking the tax law by paying you as an independent contractor and may be cheating you out of certain benefits. (While it might be a violation of immigration laws to hire you as an employee, the IRS does not inform to ICE. The IRS requires that you be treated as an employee if you are one, even if you are not legally allowed to work by the immigration department.)
File your tax return using your SSN. The IRS has records that will allow them to associate your TIN and SSN.
If you really did work as an independent contractor, and were later hired as an employee, you will need to include a schedule C with your tax return for your self-employment income, while adding your W-2 wages to the main part of your return. You will pay income tax and self-employment tax on the business income. (SE tax is double the normal social security and medicare tax you see on your W-2. For employees, you pay half and the employer pays half; when you are self-employed, you pay both.)
If you were an employee the whole time, ask your employer for a corrected W-2 and to cancel the 1099. If they refuse, then enter the W-2 first on your return. When you enter the 1099-NEC, check the box on the page of special circumstances for "I received a W-2 from the same employer and this income should have been on my W-2." Turbotax will prepare a form 8919 and you will pay the employee half of social security and medicare that was not collected from your pay, but you won't have to pay both halves.
