A file with the ASE file extension is an Adobe Swatch Exchange file used to store a collection of colors accessible through the Swatches palette of some Adobe products such as Photoshop. The format makes it easy to share colors between programs.
How to open ASE swatch files in Illustrator
Autodesk software can export files with this extension to the Autodesk ASCII Scene Export format. They are used as plain text files that store information about 2D and 3D scenes. They are similar to Autodesk's ASC format, but can contain more information about things like shapes and points.
Other ASE files can be Velvet Studio Sample audio files used for storing instrument sounds, or Aseprite Sprite graphic files.
ASE files can be opened with Adobe's Photoshop, Illustrator, InDesign, and InCopy software programs, as well as the defunct Fireworks program.