Normally i see this issue occurring as an artifact from Photoshop when you cut or merge something that formerly had a gap inbetween them. As you save the file or look closer you will notice that the gaps aren’t there anymore.
But i recall importing grouped shapes from illustrator and this thin gap was an actual issue, causing trouble even with layer styles. My solution there was to import the pieces separately and merging them in photoshop instead, but in your case it will take forever to import each piece of this.
Another way would be applying a very tiny offset path to it so it will overlap with each other, or filling a block of color behind it.