Have you tried searching for Birmingham schools in SchoolFinder? http://www.education.com/schoolfinder
Individual school listings will reference if the school provides special education services. For instance, if you meant Birmingham, Alabama, here's a special education school that serves children in grades pre-K through 12th. Contact the local schools (or the district) to learn more about local school programs and accommodations for children with ADHD. I also suggest talking with your child's pediatrician for referral to local schools or programs that could be a fit for your child.
Below is some additional information you may find helpful. Thanks for asking!