How can I record dependent care assistance program on Schedule C and also have form 2441 part 3 populate?

Dependent Care Benefits are shown in box 10 of a W2. Do you have employees you provide Dependent Care Benefits for? Did your Self-Employment business provide Dependent Care Benefits?

Part 3 of Form 2441 is used to reconcile any Dependent Care Benefits that were used to qualifying Dependent Care Expenses.

I need a bit more information to give you further advice.

Publication 503 (2022), Child and Dependent Care Expenses

A dependent care assistance plan or flexible spending account (FSA)  is provided from an employer to an employee. Unless you have a business that supplies these benefits to your employees, Schedule C does not apply to this situation. 

@leeloo is correct. A Dependent Care Assistance Program is a Flex Spending Account (FSA) offered through your employer. If you received dependent care benefits as an employee, they should be shown in box 10 of your Form W-2, Wage and Tax Statement. Benefits you received as a partner should be shown in box 13 of your Schedule K-1 (Form 1065) with code O.

Here are the steps to enter the information for Form 2441:

• Sign into TurboTax and select Pick up where you left off.
• At the right upper corner, in the search box, type in childcare and Enter
• Select  Jump to childcare
• Follow prompts

If you are the owner of a small business, I'm pretty sure you can't give yourself dependent care benefits.  There are limits on section 125 cafeteria plans, they can't be used by owners (to the best of my memory).