How to merge layers with different blending modes into one layer in photoshop ?

When you merge layers, any blending modes applied to the layers should be applied permanently by the merge, so this should be no problem; their effect should be permanently visible in the merged result.

If your question is really about preserving a blending mode so that it’s carried with an exported PNG file and applied wherever that PNG file is used later, that isn’t possible with Photoshop or any other image editor. The limitation is that PNG (and other image file formats) don’t support blending mode info for other apps to use. Blending modes are applied by whatever is compositing the image (photo app, video editor, web page…).

For example, if you intend to use a PNG file on a web page and you want it to use the Multiply blending mode over the web page background, the PNG file format does not provide a way to store that blending mode, so Multiply must be applied in the web page code that handles that image.