The Dodge Tool and the Burn Tool can be used to refine the edge of a mask by darkening or lightening the grey areas at the edge of a mask to make a more precise edge. The Smudge Tool can be used to push in the outline where an edge does not need to be sharp, such as a slightly out of focus area.
Try to blur any selected edge to the same amount as it was sharp in the original photo.
Blur and Increase Contrast. Select an edge e.g. with a Lasso. Blur with a Gaussian Blur which blurs and smoothes the edge, then increase the contrast with Image > Adjustments > Brightness/Contrast. The Legacy setting may be stronger. (Piximperfect).
Sometimes blending works better if a little of the background colour is painted over the edges.
Green Screen Colour Fringe Removal
Select > Colour > Use the eyedropper to select the green and the fuzziness to refine the edge. (Using Composite Photography to Create a Fantasy World by Karen Alsop)