Sorry, that's self-employment. The fact that it must be approved by your regular employee does not mean you are an employee of the outside firm that hires you.
If you are doing side jobs for outside groups, and you think you should be classified as an employee of those outside groups rather than a contractor, start by reading these documents.
https://www.irs.gov/businesses/small-businesses-self-employed/independent-contractor-self-employed-o...
To classify your income as employee wages rather than contractor payments, you would need to include form SS-8 with your tax return. You must provide detailed information about the type of work, how your work is controlled or assigned, and how you are paid. You would also file form 8919 to report the uncollected social security and medicare taxes. With form 8919, you would pay 7.65% employment tax instead of 15.3% self-employment tax.
https://www.irs.gov/forms-pubs/about-form-8919
https://www.irs.gov/forms-pubs/about-form-ss-8
You would have to file a separate SS-8 form for each job where you think you are an employee rather than a contractor. You would file one overall form 8919. In Turbotax, when entering the 1099, check the box for "this was wages that should have been on a W-2" and use reason code G "I filed Form SS-8 with the IRS and haven’t received a reply yet."
For SS-8 will start an investigation of you and the company you file against. If the IRS determines you were an employee, the company can face significant penalties. If the IRS determines you were a contractor, you will have to re-file your tax returns and can be subject to interest and late fees on the taxes you owe.
