What is an ASE File? 
How to Open, Edit, and Convert ASE Files

A file with the ASE file extension is an Adobe Swatch Exchange file used for saving a collection of colors accessed through the Swatches palette of some Adobe products like Photoshop. The format makes it easy to share colors between programs.


How to Open an ASE File

ASE files can be opened with Adobe's Photoshop, Illustrator, InDesign, Fireworks, and InCopy software.

This is done through the Swatches palette, which you can open via the Window > Swatches menu. Select the small menu button to the top right of the palette and then click Load Swatches... (it's called Open Swatch Library... in Illustrator and Add Swatches... in Fireworks).

Note: If you can't find the ASE file, be sure that the "Files of type:" option is set to Swatch Exchange (*.ASE), else you may be filtering the results for other files by mistake, like ACO or ACT files.

You can author Adobe Swatch Exchange files at Adobe Color CC, which you can then download in the ASE format.

Source: https://www.lifewire.com/ase-file-2619688