What sort of sheet this covers
A medical certificate is any short sheet in which a doctor states a fact about your health. It might say that you are fit for a job, that you had a jab, or that a child may join a sports club. It may come from a public clinic or from a private surgery. The wording matters less than the signature at the foot, because that signature is what the stamp really covers.
The signature must be one the office can trace
The Prefettura, the state's local office in the province, keeps sample signatures of public officials. Its clerk lays your sheet beside the sample and looks for a match. A doctor employed by the public health service is usually on that list already. A doctor in a private surgery often is not, so ask at the counter which extra confirmation it wants before you queue.
That is the real answer to how to apostille a Medical Certificate without delay: settle the signature first. Once the clerk can trace the doctor, the stamp itself is a short job at the desk. Court rulings and notary deeds go somewhere else, to the Procura della Repubblica, so a doctor's sheet never joins that queue.
How fresh the sheet has to be
No clerk stamps an expiry, but the office reading your file abroad often has one in mind. Plenty of visa desks and schools will only look at a sheet signed a few weeks back. So collect the doctor's paper, then apostille a Medical Certificate in Bari rather than leave it in a drawer. If the sheet goes stale you pay the doctor again, and you buy the stamp again as well.
What you pay
The apostille cost for a Medical Certificate in Bari is the €16 tax stamp, bought at a tobacconist and handed in with the sheet. Some papers are exempt from it, and the clerk will tell you so when you reach the front. Past the stamp there is nothing else to settle at that counter. No waiting time is published, so allow for more than one trip.
Who reads it on the far side
Think about the reader. A works doctor, an insurer, a school office or a visa clerk each want different detail, so ask in writing what your doctor should state on the sheet. Then apostille a Medical Certificate in Italy in the province where the doctor signed, because the stamp follows the signature rather than your home address.
Bear in mind that the legalisation of a Medical Certificate in Bari says nothing about the words on the page. If the desk abroad cannot read the sheet as written, it will ask for a sworn version. Confirm the required language with the receiving office in writing, then have the text sworn before a court here so the wording carries an oath.