I am conducting COM pulling simulations on GROMACS. I wish to pull a protein along a helical path. For this purpose, I am setting pull-coord1-geometry = distance, and want to provide an external potential formulated in the following study: 10.1073/pnas.1307905110.
I am not sure how to write the module or in which directory to place it. It would be great if there was a sample module I could follow, or if I could find guidelines somewhere.

We are currently working on restructuring the code, so that writing that type of potential is easier, but are not done yet. Oliver Fleetwood has written some extension to GROMACS where you can add arbitrary mathematical expressions for pull coordinates - the main idea is documented here

To go into more detail on your reference, I assume you want to implement the following potential?

The umbrella potential is U ( u , r ) = ku / L ( r ), and its force components are Fu = −2 ku / L and Fr = −8 πkur ( θL −2 πu )/ L 4. Here k is a force constant; u and r denote the deviation from a reference point ℧ in the helical and the radial direction, respectively; L is the r -dependent length of a full helical turn; and θ is the angular distance to a reference point.

So you want to transform an angle pull-coordinate and a distance pull-cordinate into a more complicated potential? This should indeed be possible once my changes mentioned by Christian are available in GROMACS.