The phrase "diagnosed disability" means that a medical professional has determined and confirmed that a person has a physical or mental condition that affects their abilities or functioning in some way. Full definition
The only exception is for approved students with diagnosed disabilities who can not hand write the essay. (act.org)
Some children and young people have other medically diagnosed disabilities which may impact upon their learning. (lambeth.gov.uk)
The gap grows as they progress through school primarily because of differences in the proportion of students classified as having a Specific Learning Disability (SLD), which he reports is for most students a relatively mild and subjectively diagnosed disability. (educationnext.org)