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In the Effects panel, you could try changing the blend mode of the PNG from Normal to Darken or Multiply.
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Can I please ask for your advice?
When the art is black & white like a signature, you don't need to use transparency. Here, on the right, I've saved your art as a 1-bit (Bitmap mode) .psd with the .psd's frame set to no fill. In this case there would be no transparency on the page.
You can also save as Grayscale and use Multiply if the image needs to be over multiple color fills (center). Or, with the image set to black and the frame set to the desired background color (left).
If the destination is a printing press, all of these options would be better than .PNG because PNG has to be RGB and will output as a 4-color mix.
Thank you everyone for your help, I was able to resolve the problem earlier by converting artwork to a vector graphic. I did try to use the instructions from Bob post, it didn't work for me unfortunately,
Thank you for your comments, I've learned new things thanks to you