You would need to create a world-space ray by unprojecting the normalized device coordinates of the mouse click position and then do a ray-plane intersection. Assuming an intersection occurs, all you would need to do is then transform this world space intersection point into the area encompassed by your ground plane grid and then do what you want from there.
he problem I don't get is how can I check that it intersept a certain area on my plane?
You need 2 extra direction vectors + a position to define a coordinate frame. As an example, consider the grid centred at position (0,1,0) - let's call that 'W', with the plane normal also pointing up in 'Y' (0,1,0). We need to define the 2 directions for your plane (i.e. the +X, and +Z directions).
Compute your intersection point on the plane.
IP = getIntersectPointOnPlane(plane, selection_ray);
Make the intersect point relative to the grid centre, i.e.
IP_relative = IP - W
Now compute the X and Z coordinates using a dot product.
Another option, since you're going to want to color/texture the chosen area, is to break the plane into many individual triangles/quads, and then you wouldn't need to know where on a triangle(or the plane as a whole) the ray intersects; just which triangle, and color/texture it (and it's neighbor) accordingly.