This is anything but sure because you haven't revealed what "put on screen " means.
I guess you have a partially transparent layer which has complex black and white gradient patterns. On a background layer they look not so pleasant:
But if you set the blending mode =Screen, the effect is what's wanted:
Now you search a way to store the decorative shape layer as partially transparent PNG so that it would give the wanted effect when it's layered on a background WITHOUT other blending than normal. That's a little peculiar because blending mode Screen should be supported in web browsers and all pro level image and video editing programs. But you will get it.
1) rasterize the Black and white shape layer, select all and copy the layer content to clipboard. Shut the shape layer.
2) create a new layer, fill it with white and give to it a layer mask
3) fill the layer mask with black; you can reach the layer mask by clicking its icon in the layers panel
4) take the layer mask to onscreen editing by clicking its icon and holding Alt key at the same time
5) paste in place the shape from the clipboard. Click again the image icon in the layers panel and then the layer mask icon to get the mask for off-screen editing. Apply curves to the mask for wanted effect depth:
Without curves the black seems to fade a little too fast.
Now you can shut the background layer and save as PNG. The result is usable as overlay with normal blend mode.