Is it possible to have the Feather tool as 0.5 pixel in Photoshop

It depends on what your intentions are with the selection. For example, if you apply a filter then you can go Edit > Fade the Opacity of the adjustment/edge.

Nothing can be half a pixel, ever, end of story. The pixel is the atom, and no, there are no quarks here.

But you can still feather to fractional pixels like above. That's how it works. It may not be "half a pixel", but the gross effect is the same.

This is how it's done:

Hi there,

Thanks for reaching out to us!

It seems like a great idea, could you share this as a feature request here? https://feedback.photoshop.com/photoshop_family/categories/photoshop_family_photoshop 

This forum is monitored by our developers and they might look into it for future updates.

Regards,

Akash

perhaps a half-selected pixel fades half as much. Fractional handling of edges is one trick in the armoury for smoothing edges.