The phrase "a special degree" is correct and usable in written English.
It can be used when referring to a specific level of education or qualification that is distinct or unique in some way.
Example: "She earned a special degree in environmental science that focuses on sustainable practices."
Alternatives: "a unique qualification" or "an exceptional credential".
The freshwater shijimi clams solicited a special degree of disbelief.
"People treated her recollections and interpretations of doctrine with a special degree of reverence," he said.
Acheson met these criteria to a special degree and did so with zest".
But in 1989 Brown gave him a special degree, a Bachelor of Philosophy, for his "sustained service to the university".
The business, which had been operating since 2007, provided a special degree of care and attention to guests, who were invited into her home and treated as members of the family.
Employers in many industries -- especially those that do not require a special degree, like law or medicine -- enjoy hiring older people because they are often more focused and know what they can and cannot do.
Patients need not be referred with any special degree of severity or case-mix.
The highest level of secondary education completed is measured by a set of dummy variables, distinguishing respondents who have either no completed degree in secondary education or a special education degree (=1), a lower secondary education degree (=2), a degree of higher secondary education in a vocational track (=3) or a degree in a general or academic higher secondary level (=4).
Nitrogen adsorptiondesorption experiments revealed a certain but special degree of mesoporosity in the modified char with an average pore size of 3.24 nm.
A master's degree in physician assistant studies doesn't require a special undergraduate degree.
In his spare time, he studied for a special honours degree at London University.
