I am writing a report about an assessment, the subject of the assessment is a large group of patients and their health. The report refers to the patients repeatedly. my question is : how proper/common/fitting/understood the word "assessee" would be ?
Better terms would be "participants" or "subjects." Even "evaluees" is used more commonly than "assessees," but it would not be the optimal term (try searching for each of these terms on pubmed.gov for a very crude gauge of the comparative numbers). (I do not think I had ever encountered "assessees" before reading the question here.) Note that "participants" somewhat implies that participation in the assessment was voluntary, whereas "subjects" does not carry that implication. (For example, it would be inappropriate to use "participants" in a report discussing an analysis of cadavers, but "subjects" could be used in such a report.)
Another option, if a single word is not required, would be to use a phrase such as "evaluated patients," "assessed patients," or "patients available for assessment."
Take a look at some of the reports available through the websites for the US National Health and Nutrition Examination Survey (NHANES), the Health Survey for England, or the Cochrane systematic reviews organization for examples.