Will being audited last year for proof of dependency for my 3 kids effect this year's taxes? If so, what do I need to solve the issue and get the ctc?

It is possible that if you don't resolve the dependency issue on the 2020 return then they will not allow them on the 2021 return.  

It doesn't have to be a doctor's letter.

any evidence that child lives with you.

a letter from other parent indicating that you are the custodian would be good.

See IRS Form 14815-A here

https://www.irs.gov/pub/irs-pdf/f14815a.pdf

So if I provide SSN, Birth certificate and my marriage license to their mother that should cerfice? I'm new to this and have no clue what I am doing!

other documents that should be adequate 

• School records or statement.
• Landlord or property management statement.
• Health provider statement.
• Medical records.
• Child care provided records.
• Placement agency statement.
• Social service records or statement.
• Place of worship statement.
• Indian tribal official statement.
• Employer statement.
• affidavits signed by neighbors

@kyahsdad27 

"So if I provide SSN, Birth certificate and my marriage license to their mother that should cerfice?"

None of that shows support.

Did you look at item 5 in the document I posted for you?

If you can get their mother to give you a 2020 Form 8332 for years 2020 and 2021 (Part I and Part II), that should resolve your support issue for tax year 2020. You won't have an issue with your upcoming tax return.

You'll be able to e-File 2021.

Ok ... so you married the mother ?    And you are not the biological father ? 

If you are married then why did you not file a joint return with the mother?   Did you live together ?   

Did you try to claim Head of Household using this child ?

And for a child under the age of 19 support is not an issue ... the child themselves cannot be self supporting.  The IRS wants you to prove they are your kids to claim and that they lived with you for more than 1/2 the year.