I'm looking for a single word for describing someone who always speaks words incorrectly so that nobody but ones who are familiar with his disorder may understand him. I'm not sure if there is a word for this I hope there is. Thanks
There is dyslalia:
dyslalia [mass noun] Medicine
Inability to articulate comprehensible speech, especially when associated with the use of private words or sounds.
Mid 19th century: from dys- ‘difficult’ + Greek lalia speech.
Oxford Living Dictionaries
impossible to understand.
There is not a specific word for a person who speaks unintelligibly. In this field, as in many human services fields, there is a preference to use language that puts the person--not the disorder--first, in writing that is meant to be read by the client or family. In casual, non-professional conversation, you could say
Her speech is unintelligible.
The second example makes it slightly more clear that the speech itself, not the word choice or grammar, is where the problem is.
Dyslalia (M-W medical dictionary) is a term that was popular in the beginnings of the field of Speech-Language Pathology, but in the last 17 years as an SLP I have never seen the term used except in billing and diagnostic codes, which sometimes hold onto historical language. This Google Ngram shows a spike for dyslalia in the 1940s-50s, followed by declining usage.
There are other terms that are more specific about the origin of the unintelligibility, but they are specialized terms that would be unlikely to be used in casual/non-professional conversation.