Can aperture be changed in aperture mode even with a fixed aperture lens?

The f/2.8 in the name of the lens does not indicate fixed aperture in the sense of not being able to change it - it designates the widest aperture. You should still be able to set it to e.g. f/4 or f/8, but you won't be able to set it to f/2, because the maximum is f/2.8.

The sense in which it is "fixed" is that you can use f/2.8 throughout the zoom range, as opposed to a lens that has a different maximum aperture at each end of the range, like a 70-300mm f/4-5.6 lens - that has f/4 at the 70mm end and f/5.6 at the 300mm end. It's more often referred to as "constant" aperture, not "fixed".

If a lens has a fixed aperture you cannot change it. But such lenses aren't very common for interchangeable lens cameras. The most common lens of this type would be a "mirror lens", and these are usually fixed at f/5.6 or f/8 for focal lengths around 500-800mm.

If your lens has a maximum aperture of f/2.8, you almost certainly have a constant aperture zoom lens that is capable of maintaining the same maximum aperture (minimum f-number) throughout its focal length range. Constant aperture lenses can be stopped down. The numbers in the model names indicate the maximum size of the opening, not the only size of the opening.

If there is no aperture ring on the lens that just means you must use the camera's controls to change the size of the aperture in the lens at the instant of exposure. No matter what aperture you or the camera select for exposure, the lens normally stays wide open until the instant before the picture is taken. This allows for a brighter viewfinder and more sensitive and accurate autofocusing.

The terminology in your question is most likely incorrect.

Several manufacturers make a 16-35mm F/2.8 lens which is a Constant-Aperture Zoom meaning that its has the same maximum aperture at any focal-length. This means you can set it to F/2.8 at 16mm and 35mm or any focal-length in between. You can also stop it down at any focal-length. Most, if not all, constant-aperture zooms have the same minimum aperture throughout the zoom range which is nearly always F/22. Any combination of focal-length from 16 to 35mm and aperture from F/2.8 to F/22 is selectable.

Other types of lenses are:

• Variable Aperture Zoom: A zoom lens with a different maximum aperture depending on the focal-length. A typical example is an 18-55mm F/3.5-5.6 which can be opened to F/3.5 at 18mm but only up to F/5.6 at 55mm. In between, the maximum aperture varies too, so at 24mm you might be able to open up to F/4.5 for example. These lenses have a minimum aperture which can but don't always vary, say F/22 at 18mm and F/32 at 55mm.
• Prime: A lens with a fixed focal-length which normally can change its aperture from a certain maximum to a minimum. Typical example would be a 50mm F/1.4 which can have its aperture set from F/1.4 to F/16, but other ranges are possible
• Fixed Aperture: This type of lens lacks an iris mechanism and hence its aperture is fixed. These are always prime lenses as far as I know which is logical since the size of the aperture would have to change as you zoom to maintain a fixed aperture at all focal-lengths. These lenses are rare and mostly old models but a few modern ones exist such as the Canon RF 800mm F/11 IS STM released this year.