In total, 140 people who were given their extra dose of the Moderna Covid-19 vaccine in the Gorebridge vaccine centre in Midlothian were affected by the error.
Health authorities have maintained there is no risk to individuals due to the error and that half a dose will provide sufficient protection.
The individuals affected were all immunosuppressed, the Midlothian Health and Social Care Partnership said, meaning they are more vulnerable to infection and at higher risk from serious complications caused by Covid-19.
The HSCP apologised for the mistake and any anxiety caused.
Advice from the Joint Committee on Vaccination and Immunisation recommended a third primary dose of the vaccine for immunosuppressed individuals as part of the wider booster jag rollout for older people and those previously on the shielding list.
Booster jag rollout began on September 20, with the errors taking place over two days on October 4 and 5.
Individuals affected were first contacted by the HSCP last week with letters being sent by health officials to patients.
Morag Barrow, Director of Health and Social Care for Midlothian Health and Social Care Partnership (HSCP) said: “On Monday 4 October and Tuesday 5 October2021, 140 patients who are immunosuppressed were given a half third dose of the Moderna vaccine rather than a full third dose.
"Expert scientific evidence is clear that this will not cause any harm and will still ensure sufficient robust protection.
"All those affected have been contacted and we would like to apologise for any anxiety the error may have caused.
“All procedures, guidance and training around the Covid vaccination programme at Gorebridge have been reviewed, and lessons learned have been implemented and will be shared with peers nationally.”
In total, 4,289,119 people have received their first dose of a Covid-19 vaccination and 3,879,942 have received a second dose during the rollout of the vaccine in Scotland.
Almost 30,000 people who are severely immunosuppressed have received a third dose of the vaccine.
JCVI advice states that the benefit of a third dose is unknown, but recommends a third dose on the basis that it may provide a benefit and be unlikely to cause any harm to the patient.
Ian Murray, Labour MP for Edinburgh South, said: "This error will cause concern among many.
"It's vital that measures are immediately taken to rectify the situation.
"From cover-ups and the vaccine passport chaos to pensioners travelling miles for a flu jab, the SNP government has repeatedly undermined public confidence, which is deeply disappointing and demonstrates why ministers' focus must remain on the ongoing situation."
A Scottish Government spokesperson said: “We are aware of this error in the application of vaccine dosage for a specific cohort of patients in Midlothian on October 4 and 5, and that the Health and Social Care partnership in Midlothian have rightly apologised to all the patients who were affected.
“It is welcome that clinical advice is that this will not have caused harm to any patient. The incident is being fully investigated so that lessons can be learned and there is no repeat.”