I don't know if there is a more cleaver technical way to overide the order of the media library listing, but perhaps you could look at Powerslice (free Episerver Addon) that enables you to 'slice' through your data by types, terms, and facets. It is powered by find, so perhaps as part of building the slice you would want to order the items appropriately. Its not exactly what you describe you need, but perhaps can give you some inspiration or alternative to what you are asking for.

To check the properties of the image, open it (it will open in 'On page' mode, and then select 'All Properties' to see the associated properties for that media type and their values.

Hi Himshikhar,

I think you can achieve this by creating a custom event handler. Similar to this. You can do this for your ImageMedia type. I am assuming that you have created separate types for document  type and ImageMedia type.

Get all ImageMedia types (in current folder) in you PublishEvent (in reference to the code in blog) then create writable clone, now you can sort them. At Last step, save back.

You have two different requirements,

1. Sorting on date: You can sort on Created property or create a custom PublishDate property (in your ImageMedia type) to then sort on that.
2. Check the properties of the image or doc: That is already solved by checking type in event handler (Check type is ImagMedia).