Downhole swivel sub and method for releasing a stuck object in a wellbore

In certain embodiments, a downhole swivel sub includes a first swivel part configured to connect to a first section of a workstring, and a second swivel part configured to connect to a second section of the workstring. The second swivel part is rotatable relative to the first swivel part. The downhole swivel sub also includes a locking sleeve rotationally coupled with the first swivel part and movable axially between a locking position wherein the first swivel part and the second swivel part are rotationally coupled and an unlocking position wherein the first swivel part is rotatable relative to the second swivel part. The locking sleeve includes at least two first rows of teeth disposed at a same radial position and separated axially on the locking sleeve. The at least two first rows of teeth are configured to engage and disengage with at least two second rows of teeth located on the second swivel part.