In June, Carlton was diagnosed with cardiomyopathy. As a result of the disease, he has suffered three major strokes in the past two months, deputies said.
"The Harris County Sheriff's Office has embraced Jaden as their own and want to keep him encouraged," officials said in a Facebook post.
Carlton has a pacemaker to regulate his heart and is currently on the list for a heart transplant in June.
"Welcome to the HCSO family, Jaden," the post stated.