How can I change employment to reflect job is part time?

There is no where on a tax return where you can indicate the a job is either full time or part time.  You need to enter all income received in 2023 on your 2023 tax return.

You do not have to enter anything about the job being part-time.  You just have to enter the income you received from the job.  Do you have a W-2?  Or a 109NEC?

I'm not quite sure what you mean,

If you entered it with your initial information

1. Log into TurboTax
2. Select My Info from the menu
3. Click the down arrow next to your name
4. [EDIT]
5. You can change your occupation at the bottom of the page.

This will have no affect on your tax return.  It is used for IRS general information.