I tried printing grids on white paper using an offset sheet feed machine. I used a gray color ink. I wanted to use a fountain pen on this paper. When I wrote on this paper I found that the fountain pen ink was skipping whereever it crossed the grid lines making the writing look bad with interruptions. Can anybody help me with this problem.
Presumably the printer won't allow you to change to a water-based ink, so what you're left with is to not use a pen with water-based ink either.
I'd guess your problem really is that fountain pen ink tends to be very 'watery'. At the opposite end of the scale would be a regular plastic 'biro' but they tend to skid over any waxy surface.
This is very possibly why the 'sharpie' type 'felt pen' has become so popular… will write on anything less waxy than a candle ;)
Late edit Actually I just tested. A sharpie will write on a candle.
Offset prints inks are oil-based. That is the principle of offset printing: Water repelling the ink.
Notebooks are printed using different systems, some a little old fashioned are printing the lines with some needles that are feed with water-based ink.
Another option could be screen printing. But I am not sure about which one.