I have tried various fixes like removing doubles, altering the mesh, the problem persists. Here's the .blend: https://drive.google.com/open?id=1OwhsqAuXHCTySSfbciQxV9f1igz4xLQ1
It looks like it's a problem of normals, select all and ShiftN to recalculate and it will fix it.
I’m quite sure it’s because you have seven edges converging into one vertex.
From what I understand, the Subsurf Modifier is approximating vertex relationships not the vertexes themselves i.e. it will not move that vertex to round things off because it is rounding the space/edges between vertexes.
To have a stray vertex will definitely cause issues like this especially when tris/multiple edges are involved.
Solution: Fix the topology. Maybe use a knife tool or go in and delete some data? Basically, you should almost never have seven edges going into one vertex like that. Addressing that will probably fix your issue.