The Reserve of Byram Apartments for rent in Jackson, MS on ForRent.com: (877) 469-2796 - Availability, pricing and special promotions subject to change daily. Welcome to Reserve at Byram, located in Byram, MS. We offer 1, 2 and 3 bedroom spacious apartment homes. You will be impressed with the many features and amenities, that include, patiobalconies, alarm system, swimming pool, fireplaces, cablesatellite, washerfryer hookup, corporate units, and much more. We are where you want to be.