It comes as the coronavirus vaccination programme is being extended to cover youngsters aged between five and 11 across Scotland.
Katie Dee, deputy director of public health at NHS Lothian, said parents should still bring their children forward to be vaccinated – even if they had incorrectly been told they had an underlying health condition.
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Ms Dee stated: “We are really sorry for this admin error and are writing to the affected parents to apologise for the confusion it may cause.
“We use two letter templates in Lothian to invite children – one for children who have underlying health conditions and one for children who do not.
“It appears that the wrong version may have been used when offering some appointments to children in Midlothian and West Lothian.”
She stressed however that appointments in the letters were still valid, telling parents: “All of the appointment information remains the same and they should turn up for the appointment that has been reserved for them.”
Ms Dee added: “The numbers of people testing positive for infection have increased rapidly across Scotland and vaccination is one of the best ways to protect ourselves and our children against the virus.”