It should just attach with small screws on the sides..as long as the ceiling light was the same? post a photo of fixture you have now

Thank you for responding. It does attach with the screws that are in the plate in the ceiling. What I would like is a different shade instead of the mushroom shape glass shade.

So you need to find a shade in the shape you want with the same size fitting (3.66"). Unfortunately, these types of traditional shades are becoming less and less popular and more difficult to find. What type of shade are you wanting? And your fitting size is not common, usually they are 3" or 5", not 3.66".

Good luck and honestly these are very dated and provide really poor lighting Changing a light fixture is a very simple job that does not require an electrician at all . If wanting to do DIY go yto youtube it will wlk through the whole process.

After a little research I found what this type of shade is called: Lip Fitter Shade!

Rejuvenation has a few.