Sounds like someone has messed it up in the past. Whether you can do anything about it will depend on how long it has been like this.
Highway is land that the public has a right to travel along - different classes of highway - carriageways, footpaths and bridleways etc. Highway can come about either through historical reasons (ancient tracks - which have achieved their status through long use and hence the public has achieved a legal right of way), or because the owner has dedicated the land to be highway land. Most highway land is adopted. This means the council is responsible for maintaining it. But there are also private roads that have been adopted by the council by agreement. Some highway land in private ownership has an obligation for the landowner to maintain it - some does not. Complex isn't it.
You appear to have ownership of a private piece of highway land where the council has agreed to adopt it. Its still yours but depending on whether any agreements were entered into by previous owners, and how long this situation has existed you may, in effect, have a useless piece of land. If it has being like this for more than 20 years, 'long use' rights may have been achieved by the public to pass along the path.
You could try writing to the council to seek to clarify what they think the legal position is, but your natural desire to fence this in and move the path closer to the carriageway is likely to have to involve a legal process with expensive solicitors.