I am using ArcGIS Desktop 10.5.
What would be best solution to fill gaps and empty data when forming mosaic?
I tried mosaic, mosaic to a new rater. Not satisfactory.
Is there a way to blend with basemap?
Since the gap inherent to your source (scanned documents), there is no easy way to get rid of these gaps. If your mosaic had other images covering the same area, you would make "white" colour as background and mask it, but here this is not the case. These gaps are geographic entities, as if these areas are really represented by white colour. I think you need to remove those middle gaps either manually (by using Photoshop or GIMP), or, if you have python experience, something similar to this post, basically you need to find the white stripes by looking at RGB values and shift the raster matrix by cropping this part. If you do it manually, just Select the relevant parts with Select by Rectangle tool and paste into a new image. And then save it as a new image and then re-georeference.