For 2023, I have $4202 of capital losses that I am carrying over. It shows that I have $3000 of allowable loss but it is deducting only $1202. How can I correct this?

Which of these numbers do you see on the Form 1040, Line 7?  To see this line follow these steps:

In TurboTax Desktop - 

1. Click on Forms in the upper right corner. 
2.  Then click on 1040 in the list on the left.  
3. Scroll down the form to view Line 7

In TurboTax Online:

1. Click on Tools in the menu on the left
2. Click on Tax Tools
3. In the box that pops up on Tax Summary
4. Then click on Preview My 1040 in the menu on the left
5. Scroll down to view Line 7

If you see the $3,000 here, then the issue is with the display screen in the software but your tax return is correct.  If you do not see the $3,000 here please let us know so that we can continue to troubleshoot. 

This assumes that you do not have capital gains in 2023 that are being offset first.