The power of a Presidency Magistrate to order a prisoner in jail to be brought up for examination would depend on the laws and procedures of the specific jurisdiction. However, in many jurisdictions, including India, the Presidency Magistrate or a Magistrate empowered by the Presidency Magistrate may have the authority to issue such an order.
In India, the powers and procedures of the Presidency Magistrate are governed by the Code of Criminal Procedure (CrPC). Section 167 of the CrPC provides for the procedure to be followed when investigation cannot be completed within 24 hours. Under this section, if a person is arrested and detained in custody, the investigating officer must produce the arrested person before the nearest Magistrate within 24 hours of arrest.
Furthermore, Section 167(2) of the CrPC allows the Magistrate to authorize the detention of the arrested person beyond the initial 24 hours for a maximum period of 15 days, if the Magistrate is satisfied that sufficient grounds exist for such detention. During this period, the Magistrate also has the power to order the prisoner to be brought up for examination if deemed necessary.
It is important to note that specific procedures and powers may vary depending on the jurisdiction and the relevant laws applicable. Therefore, it is advisable to consult the specific laws and regulations of the relevant jurisdiction to determine the exact powers of a Presidency Magistrate in ordering the examination of a prisoner in jail.