I had my fourth child in 2020. Am I able to claim recovery rebate credit for him since he didn’t get the 2020 stimulus payments or is the maximum number of dependents 3?

You are thinking of the limit of three children for whom you can receive earned income credit,  That rule does not apply to the stimulus money.

Children born in 2020 were not included in the 1st stimulus because those checks were based on 2018 or 2019. No one got stimulus money for babies born in 2020 because the IRS did not know about those babies or have their SSN’s. But on your 2020 tax return you can claim your child born in 2020 for the stimulus money, as well as the other child-related credits.  You enter your new dependent in My Info.  When you go through the screens in My Info make sure to say your child lived with you the WHOLE year.  When it asks the oddly worded question about whether your child paid for over half their own support say NO.

The stimulus check is an advance on a credit you can receive on your 2020 tax return.  If something went wrong or you did not get the stimulus check in 2020, you can get it when you file your 2020 return in early 2021

The Recovery Rebate Credit will be found in the Federal Review section,  If you are eligible it will end up on line 30 of your 2020 Form 1040.

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-j-reconciling-on-your-2020-tax-return

https://www.irs.gov/coronavirus/coronavirus-tax-relief-and-economic-impact-payments-for-individuals-and-families