This looks like an issue with a lack of bleed edge- basically if the background color on the texture is white, it will show through at the seams around the texture patches.
Substance painter fixes this by extending the texture islands to fill the empty space upon export, but unfortunately doesn't do the same thing when it exports to photoshop files.
To fix this, I'd recommend filling the texture background with a solid fill, usually the base color of the fur. If you're still getting visible seams, it can help to paint the new texture colors a bit outside the boundaries, and you might need to clean up the edges a bit.
Sorry for the trouble here, I hope this helps with resolving it.