Rotational continuous circulation system

A rotational continuous circulation system and methods includes a circulation sub having an internal bore extending along a central axis. The circulation sub has an uphole body having a reduced outer diameter along a downhole length of the uphole body. A central valve selectively opens and closes the uphole internal bore. At least one check valve is located within a sidewall of the uphole body to selectively allow fluid to flow into the uphole internal bore through the at least one check valve. A downhole body has an uphole portion circumscribing a downhole portion of the uphole body. A sleeve assembly circumscribes the reduced outer diameter of the uphole body. The uphole body and the downhole body are configured to rotate about the central axis independently from the sleeve assembly. A side-entry port of the sleeve assembly provides a fluid flow path from an exterior of the sleeve assembly to the at least one check valve.