What is the ruling on intern doctors exchanging work shifts for a fee, and what is the ruling on a doctor signing on behalf of a colleague in this situation?

The permissibility of a doctor substituting for another depends on the hospital administration's regulations. If the administration permits it, then substitution is permissible, and the fee may be taken. If it does not permit it, then it is not permissible. Doctors must adhere to the administration's regulations, in accordance with the Almighty's saying: "O you who have believed, fulfill [all] contracts," and the Messenger's (peace be upon him) saying: "Muslims are bound by their conditions." As for the substitute doctor signing in place of the original, it is not permissible if it involves misleading the administration, because it falls under forbidden lying.