Payments are usually 60 to 90 days in arrears depending on your lease. I don’t know if the is a penalty for late payment but if there is it would also be on your lease.
I am including links to various statutes outlining the rights of royalty owners covering production from lands in the State of Texas.
These statutes can be found in Sections 91.401 to 91.406 of the Natural Resources Code concern the timely payment of royalties. Note that '91.406 provides for minimum damages and recovery of attorney's fees in a successful action to recover past due payments. Section 91.501 to 91.506 of the Natural Resources Code outline the information to which royalty owners are entitled from their payor.
If you would like the names of experienced oil and gas attorneys in your area, the State Bar of Texas has a lawyer referral service and can provide a list of lawyers board certified in oil and gas law.
As Mr. Cotten stated before. The company has 4 months to make payment on a new well. On continued production for gas they have 90 days and on oil they have 60 days. Your lease may require payment prior to the legislative terms. It may also require a different interest than the legislature. Otherwise the New York Federal Rerserve Rate plus 2%. Generally producers pay gas after 60 days and oil after 30 days.